Chapter 2 Resource Masters - Commack Schools

PDF Pass

Chapter 2 Resource Masters

Bothell, WA • Chicago, IL • Columbus, OH • New York, NY

00i_ALG1_A_CRM_C02_TP_661315.indd 100i_ALG1_A_CRM_C02_TP_661315.indd 1 12/22/10 12:30 PM12/22/10 12:30 PM

PDF Pass

connected.mcgraw-hill.com

Copyright © by The McGraw-Hill Companies, Inc.

All rights reserved. The contents, or parts thereof, may be reproduced in print form for non-profit educational use with Glencoe Algebra 1, provided such reproductions bear copyright notice, but may not be reproduced in any form for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning.

Send all inquiries to:McGraw-Hill Education8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-661315-1 MHID: 0-07-661315-1

Printed in the United States of America.

1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11

CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish.

MHID ISBNStudy Guide and Intervention Workbook 0-07-660292-3 978-0-07-660292-6Homework Practice Workbook 0-07-660291-5 978-0-07-660291-9

Spanish VersionHomework Practice Workbook 0-07-660294-X 978-0-07-660294-0

Answers For Workbooks The answers for Chapter 2 of these workbooks can be found in the back of this Chapter Resource Masters booklet.

ConnectED All of the materials found in this booklet are included for viewing, printing, and editing at connected.mcgraw-hill.com.

Spanish Assessment Masters (MHID: 0-07-660289-3, ISBN: 978-0-07-660289-6) These masters contain a Spanish version of Chapter 2 Test Form 2A and Form 2C.

0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd ii0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd ii 12/22/10 12:23 PM12/22/10 12:23 PM

PDF Pass

Contents

iii

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

Teacher’s Guide to Using the Chapter 2 Resource Masters ..........................................iv

Chapter Resources Chapter 2 Student-Built Glossary ...................... 1Chapter 2 Anticipation Guide (English) ............. 3Chapter 2 Anticipation Guide (Spanish) ............ 4

Lesson 2-1Writing Equations Study Guide and Intervention ............................ 5Skills Practice .................................................... 7Practice .............................................................. 8Word Problem Practice ...................................... 9Enrichment ...................................................... 10

Lesson 2-2Solving One-Step EquationsStudy Guide and Intervention ...........................11Skills Practice .................................................. 13

Practice ............................................................ 14Word Problem Practice .................................... 15Enrichment ...................................................... 16

Lesson 2-3Solving Multi-Step EquationsStudy Guide and Intervention .......................... 17Skills Practice .................................................. 19Practice ............................................................ 20Word Problem Practice .................................... 21Enrichment ...................................................... 22

Lesson 2-4Solving Equations with the Variable on Each SideStudy Guide and Intervention .......................... 23Skills Practice .................................................. 25Practice ............................................................ 26Word Problem Practice .................................... 27Enrichment ...................................................... 28

Graphing Calculator Activity ............................ 29

Lesson 2-5Solving Equations Involving Absolute ValueStudy Guide and Intervention .......................... 30Skills Practice .................................................. 32Practice ............................................................ 33Word Problem Practice .................................... 34Enrichment ...................................................... 35

Lesson 2-6Ratios and ProportionsStudy Guide and Intervention .......................... 36Skills Practice .................................................. 38Practice ............................................................ 39Word Problem Practice .................................... 40Enrichment ...................................................... 41

Lesson 2-7Percent of ChangeStudy Guide and Intervention .......................... 42Skills Practice .................................................. 44Practice ............................................................ 45Word Problem Practice .................................... 46Enrichment ...................................................... 47Spreadsheet Activity ........................................ 48

Lesson 2-8Literal Equations and Dimensional AnalysisStudy Guide and Intervention .......................... 49Skills Practice .................................................. 51Practice ............................................................ 52Word Problem Practice .................................... 53Enrichment ...................................................... 54

Lesson 2-9Weighted AveragesStudy Guide and Intervention .......................... 55Skills Practice .................................................. 57Practice ............................................................ 58Word Problem Practice .................................... 59Enrichment ...................................................... 60

AssessmentStudent Recording Sheet ................................ 61Rubric for Scoring Extended Response .......... 62Chapter 2 Quizzes 1 and 2 ............................. 63Chapter 2 Quizzes 3 and 4 ............................. 64Chapter 2 Mid-Chapter Test ............................ 65Chapter 2 Vocabulary Test ............................... 66Chapter 2 Test, Form 1 .................................... 67Chapter 2 Test, Form 2A ................................. 69Chapter 2 Test, Form 2B ................................. 71Chapter 2 Test, Form 2C ................................. 73Chapter 2 Test, Form 2D ................................. 75Chapter 2 Test, Form 3 .................................... 77Chapter 2 Extended Response Test ................ 79Standardized Test Practice .............................. 80Unit 1 Test ........................................................ 83

Answers ........................................... A1–A40

0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd iii0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd iii 12/22/10 12:23 PM12/22/10 12:23 PM

PDF Pass

iv

Teacher’s Guide to Using the Chapter 2 Resource Masters

The Chapter 2 Resource Masters includes the core materials needed for Chapter 2. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing, printing, and editing at connectED.mcgraw-hill.com.

Chapter Resources

Student-Built Glossary (pages 1–2) These masters are a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. Give to students before beginning Lesson 2-1. Encourage them to add these pages to their mathematics study notebooks. Remind them to complete the appropriate words as they study each lesson.

Anticipation Guide (pages 3–4) This master presented in both English and Spanish is a survey used before beginning the chapter to pinpoint what students may or may not know about the concepts in the chapter. Students will revisit this survey after they complete the chapter to see if their perceptions have changed.

Lesson Resources

Study Guide and Intervention These masters provide vocabulary, key concepts, additional worked-out examples and Check Your Progress exercises to use as a reteaching activity. It can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent.

Skills Practice This master focuses more on the computational nature of the lesson. Use as an additional practice option or as homework for second-day teaching of the lesson.

Practice This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems. Use as an additional practice option or as homework for second-day teaching of the lesson.

Word Problem Practice This master includes additional practice in solving word problems that apply the concepts of the lesson. Use as an additional practice or as homework for second-day teaching of the lesson.

Enrichment These activities may extend the concepts of the lesson, offer an historical or multicultural look at the concepts, or widen students’ perspectives on the mathematics they are learning. They are written for use with all levels of students.

Graphing Calculator, TI-Nspire, or Spreadsheet Activities These activities present ways in which technology can be used with the concepts in some lessons of this chapter. Use as an alternative approach to some concepts or as an integral part of your lesson presentation.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd iv0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd iv 12/22/10 12:23 PM12/22/10 12:23 PM

PDF Pass

v

Assessment Options

The assessment masters in the Chapter 2 Resource Masters offer a wide range of assessment tools for formative (monitoring) assessment and summative (final) assessment.

Student Recording Sheet This master corresponds with the standardized test practice at the end of the chapter.

Extended Response Rubric This master provides information for teachers and students on how to assess performance on open-ended questions.

Quizzes Four free-response quizzes offer assessment at appropriate intervals in the chapter.

Mid-Chapter Test This 1-page test provides an option to assess the first half of the chapter. It parallels the timing of the Mid-Chapter Quiz in the Student Edition and includes both multiple-choice and free-response questions.

Vocabulary Test This test is suitable for all students. It includes a list of vocabulary words and 9 questions to assess students’ knowledge of those words. This can also be used in conjunction with one of the leveled chapter tests.

Leveled Chapter Tests• Form 1 contains multiple-choice

questions and is intended for use with below grade level students.

• Forms 2A and 2B contain multiple-choice questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Forms 2C and 2D contain free-response questions aimed at on grade level students. These tests are similar in format to offer comparable testing situations.

• Form 3 is a free-response test for use with above grade level students.

All of the above mentioned tests include a free-response Bonus question.

Extended-Response Test Performance assessment tasks are suitable for all students. Sample answers and a scoring rubric are included for evaluation.

Standardized Test Practice These three pages are cumulative in nature. It includes three parts: multiple-choice questions with bubble-in answer format, griddable questions with answer grids, and short-answer free-response questions.

Answers• The answers for the Anticipation Guide

and Lesson Resources are provided as reduced pages.

• Full-size answer keys are provided for the assessment masters.

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd v0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd v 12/22/10 12:23 PM12/22/10 12:23 PM

0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd vi0ii_0vi_ALG1_A_CRM_C02_FM_661315.indd vi 12/22/10 12:23 PM12/22/10 12:23 PM

Ch

apte

r R

eso

urc

es

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Student-Built Glossary2

PDF Pass

Chapter 2 1 Glencoe Algebra 1

This is an alphabetical list of the key vocabulary terms you will learn in Chapter 2. As you study the chapter, complete each term’s definition or description. Remember to add the page number where you found the term. Add these pages to your Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary TermFound

on PageDefi nition/Description/Example

dimensional analysisduh·MEHNCH·NUHL

equivalent equations ih·KWIHV·luhnt

formula

identity

multi-step equation

(continued on the next page)

001_012_ALG1_A_CRM_C02_CR_661315.indd 1001_012_ALG1_A_CRM_C02_CR_661315.indd 1 12/22/10 12:18 PM12/22/10 12:18 PM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Student-Built Glossary (continued)2

PDF Pass


Vocabulary TermFound

on PageDefi nition/Description/Example

percent of change

proportionpruh·POHR·shun

rate

ratio

scale model

solve an equation

unit rate

weighted average


Ch

apte

r R

eso

urc

es

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Anticipation GuideLinear Equations

2

PDF Pass


Before you begin Chapter 2

• Read each statement.

• Decide whether you Agree (A) or Disagree (D) with the statement.

• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).

After you complete Chapter 2

• Reread each statement and complete the last column by entering an A or a D.

• Did any of your opinions about the statements change from the first column?

• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.

STEP 1A, D, or NS

StatementSTEP 2A or D

1. When writing equations the phrases as much as, is, and is identical to, all suggest the equals sign.

2. The solving an equation strategy cannot be used if an equation is not given in the problem.

3. Given a true equation, any value can be added or subtracted to both sides resulting in a true equation.

4. Since the equation t - 23 = 54 involves subtraction, subtraction would be used to solve for t.

5. To solve 21 = -7x, you could divide by -7 or multiply by - 1 −

7 .

6. To solve equations with more than one operation, undo operations in the same order as the Order of Operations.

7. Equations with the variable on both sides have no solution.

8. 3 to 5, 3:5, and 3 −

5 are all examples of ratios.

9. Because 5 � 12 = 15 � 4, 12 −

15 is in proportion to 4 −

5 .

10. A percent of change is found by dividing the amount of change by the original amount.

11. Equations containing two variables cannot be solved since variables cannot be added or subtracted from each side of the equation.

12. To find a weighted average, extremely high or low values are not included.

Step 1

Step 2


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NOMBRE FECHA PERÍODO

Ejercicios preparatoriosEcuaciones lineales

2

PDF 2nd

Antes de comenzar el Capítulo 2

• Lee cada enunciado.

• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.

• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta, escribe NS (No estoy seguro(a)).

Después de completar el Capítulo 2

• Vuelve a leer cada enunciado y completa la última columna con una A o una D.

• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?

• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con los enunciados que marcaste con una D.

PASO 1A, D o NS

EnunciadoPASO 2A o D

1. Al escribir ecuaciones, los enunciados: tanto como, es y es idéntico a, sugieren el signo de igualdad.

2. Al resolver un problema, no se puede usar una estrategia de ecuación si el problema no incluye una ecuación.

3. Dada una ecuación verdadera, se puede sumar y restar cualquier valor de ambos lados de la ecuación, lo cual resulta en una ecuación verdadera.

4. Puesto que la ecuación t - 23 = 54 implica sustracción, éstase usaría para despejar t.

5. Para resolver 21 = -7x, podrías dividir entre -7 o multiplicar por - 1 −

7 .

6. Para resolver ecuaciones con más de una operación, anula las operaciones en el mismo orden en que lo establece el orden de las operaciones.

7. Ecuaciones con la variable en ambos lados no tienen solución.

8. 3 a 5, 3:5 y 3 −

5 son todos ejemplos de razones.

9. Dado que 5 � 12 = 15 � 4, 12 −

15 está en proporción a 4 −

5 .

10. Un porcentaje de cambio se encuentra dividiendo la cantidad de cambio entre la cantidad original.

11. Ecuaciones que contienen dos variables no pueden resolverse porque las variables no se pueden sumar o restar de cada lado de la ecuación.

12. Para calcular el promedio ponderado, no se incluyen los valores extremadamente altos o bajos.

Capítulo 2 4 Álgebra 1 de Glencoe

Paso 1

Paso 2

001_012_ALG1_A_CRM_C02_CR_661315.indd 4001_012_ALG1_A_CRM_C02_CR_661315.indd 4 12/23/10 11:58 AM12/23/10 11:58 AM

Less

on

2-1

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Study Guide and InterventionWriting Equations

2-1

PDF Pass


Write Equations Writing equations is one strategy for solving problems. You can use a variable to represent an unspecified number or measure referred to in a problem. Then you can write a verbal expression as an algebraic expression.

Translate each sentence into an equation or a formula.

a. Ten times a number x is equal to 2.8 times the difference y minus z.10 × x = 2.8 × ( y - z)The equation is 10x = 2.8( y - z).

b. A number m minus 8 is the same as a number n divided by 2.m - 8 = n ÷ 2The equation is m - 8 = n −

2 .

c. The area of a rectangle equals the length times the width. Translate this sentence into a formula.Let A = area, ℓ = length, and w = width.Formula: Area equals length times width. A = ℓ × wThe formula for the area of a rectangle is A = ℓw.

Use the Four-Step Problem-Solving Plan.POPULATION The population of the United States in July 2007 was about 301,000,000, and the land area of the United States is about 3,500,000 square miles. Find the average number of people per square mile in the United States.

Step 1 Read You know that there are 301,000,000 people. You want to know the number of people per square mile.

Step 2 Plan Write an equation to represent the situation. Let p represent the number of people per square mile.

3,500,000 × p = 301,000,000Step 3 Solve 3,500,000 × p = 301,000,000.

3,500,000p = 301,000,000 Divide each side by

p = 86 3,500,000.

There are 86 people per square mile.Step 4 Check If there are 86 people per square

mile and there are 3,500,000 square miles, 86 × 3,500,000 = 301,000,000. The answer makes sense.

ExercisesTranslate each sentence into an equation or formula.

1. Three times a number t minus twelve equals forty.

2. One-half of the difference of a and b is 54.

3. Three times the sum of d and 4 is 32.

4. The area A of a circle is the product of π and the radius r squared.

5. WEIGHT LOSS Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds.

a. If p represents the number of pounds he wants to lose, write an equation to represent this situation.

b. How many pounds does he need to lose to reach his goal?

Example 2Example 1


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Study Guide and Intervention (continued)

Writing Equations

2-1

PDF Pass


Write Verbal Sentences You can translate equations into verbal sentences.

Translate each equation into a sentence.

a. 4n - 8 = 12.

4n - 8 = 12Four times n minus eight equals twelve.

b. a2 + b2 = c2

a2 + b2 = c2

The sum of the squares of a and b is equal to the square of c.

ExercisesTranslate each equation into a sentence.

1. 4a - 5 = 23 2. 10 + k = 4k

3. 6xy = 24 4. x2 + y2 = 8

5. p + 3 = 2p 6. b = 1 −

3 (h - 1)

7. 100 - 2x = 80 8. 3(g + h) = 12

9. p2 - 2p = 9 10. C = 5 −

9

(F - 32)

11. V = 1 −

3

Bh 12. A = 1 −

2

hb

Example


Less

on

2-1

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Skills PracticeWriting Equations

2-1

PDF Pass


Translate each sentence into an equation.

1. Two added to three times a number m is the same as 18.

2. Twice a increased by the cube of a equals b.

3. Seven less than the sum of p and t is as much as 6.

4. The sum of x and its square is equal to y times z.

5. Four times the sum of f and g is identical to six times g.

Translate each sentence into a formula.

6. The perimeter P of a square equals four times the length of a side �.

7. The area A of a square is the length of a side � squared.

8. The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.

9. The area A of a circle is pi times the radius r squared.

10. The volume V of a rectangular prism equals the product of the length �, the width w, and the height h.


11. g + 10 = 3g 12. 2p + 4t = 20

13. 4(a + b) = 9a 14. 8 - 6x = 4 + 2x

15. 1 −

2 (f + y) = f - 5 16. k2 - n2 = 2b

Write a problem based on the given information.

17. c = cost per pound of plain coffee beans 18. p = cost of dinner c + 3 = cost per pound of flavored coffee beans 0.15p = cost of a 15% tip 2c + (c + 3) = 21 p + 0.15p = 23


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Practice Writing Equations

2-1

PDF Pass



1. Fifty-three plus four times b is as much as 21.

2. The sum of five times h and twice g is equal to 23.

3. One fourth the sum of r and ten is identical to r minus 4.

4. Three plus the sum of the squares of w and x is 32.

Translate each sentence into a formula.

5. Degrees Kelvin K equals 273 plus degrees Celsius C.

6. The total cost C of gas is the price p per gallon times the number of gallons g.

7. The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.


8. r - (4 + p) = 1 −

3 r 9. 3 −

5 t + 2 = t

10. 9(y2 + x) = 18 11. 2(m - n) = x + 7

Write a problem based on the given information.

12. a = cost of one adult’s ticket to zoo 13. c = regular cost of one airline ticketa - 4 = cost of one children’s ticket to zoo 0.20c = amount of 20% promotional discount

2a + 4(a - 4) = 38 3(c - 0.20c) = 330

14. GEOGRAPHY About 15% of all federally-owned land in the 48 contiguous states of the United States is in Nevada. If F represents the area of federally-owned land in these states, and N represents the portion in Nevada, write an equation for this situation.

15. FITNESS Deanna and Pietra each go for walks around a lake a few times per week. Last week, Deanna walked 7 miles more than Pietra.

a. If p represents the number of miles Pietra walked, write an equation that represents the total number of miles T the two girls walked.

b. If Pietra walked 9 miles during the week, how many miles did Deanna walk?

c. If Pietra walked 11 miles during the week, how many miles did the two girls walk together?


Less

on

2-1

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Word Problem PracticeWriting Equations

2-1

PDF Pass


1. HOUSES The area of the Hartstein’s kitchen is 182 square feet. This is 20% of the area of the first floor of their house. Let F represent the area of the first floor. Write an equation to represent the situation.

2. FAMILY Katie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation to represent the situation.

3. GEOMETRY The formula F + V = E + 2 shows the relationship between the number of faces F, edges E, and vertices V of a polyhedron, such as a pyramid. Write the formula in words.

Face

Vertex Edge

4. WIRELESS PHONE Spinfrog wireless phone company bills on a monthly basis. Each bill includes a $29.95 service fee for 1000 minutes plus a $2.95 federal communication tax. Additionally, there is a charge of $0.05 for each minute used over 1000. Let m represent the number of minutes over 1000 used during the month. Write an equation to describe the cost p of the wireless phone service per month.

5. TEMPERATURE The table below shows the temperature in Fahrenheit for some corresponding temperatures in Celsius.

Celsius Fahrenheit

-20° -4°

-10° 14°

0° 32°

10° 50°

20° 68°

30° 86°

a. Write a formula for converting Celsius temperatures to Fahrenheit temperatures.

b. Find the Fahrenheit equivalents for 25ºC and 35ºC.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment2-1

PDF Pass


Guess the NumberThink of a number. Add five to your number. Now, double your result. Double your result again. Divide you answer by four. Finally, subtract your original number. Your result is five.

How is it possible to know what the answer is without knowing the original number? Write the steps listed above as an expression in equation form. Then use algebra to show why this trick works.

Think of a number: x

Add five to your number: x + 5

Double your result: 2(x + 5)

Double your result again: 2(2(x + 5))

Divide you answer by four: 2(2(x + 5)) −

4

Subtract your original number: 2(2(x + 5)) −

4 - x

Simplify the final expression: 4(x + 5) −

4 - x Multiply.

x + 5 - x Divide.

5 Simplify.

So, the result will always be five, no matter what the starting number is.

Write variable expressions to determine why each number trick works.

1. Think of a number. Add eight. Double your result. Next, subtract 16. Finally, divide your result by 2. You get your original number back.

2. Think of a number. Multiply by 10. Add 5 to your result. Next, subtract 3. Then add 2. Next, subtract 4. Divide your result by 5. Finally, subtract your original number. Your result is your original number.

3. Think of a number. Add 1. Multiply your result by 6. Now, double your result. Next, divide your result by 12. Finally, subtract your original number. Your result is 1.

4. Think of a number. Multiply by 5. Add five to your result. Now, divide by 5. Subtract 1 from your result. Finally, subtract your original number. Your final result is 0.

5. Think of a number. Add 30. Multiply by 3. Multiply again by 2. Divide your result by 6. Finally, subtract your original number. Your answer is 30.


Less

on

2-2

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-2

2-2 Study Guide and Intervention Solving One-Step Equations

PDF Pass


Solve Equations Using Addition and Subtraction If the same number is added to each side of an equation, the resulting equation is equivalent to the original one. In general if the original equation involves subtraction, this property will help you solve the equation. Similarly, if the same number is subtracted from each side of an equation, the resulting equation is equivalent to the original one. This property will help you solve equations involving addition.

Addition Property of Equality For any numbers a, b, and c, if a = b, then a + c = b + c.

Subtraction Property of Equality For any numbers a, b, and c, if a = b, then a - c = b - c.

Solve m - 32 = 18.

m - 32 = 18 Original equation

m - 32 + 32 = 18 + 32 Add 32 to each side.

m = 50 Simplify.

The solution is 50.

Solve 22 + p = -12.

22 + p = -12 Original equation

22 + p - 22 = -12 - 22 Subtract 22 from each side.

p = -34 Simplify.

The solution is -34.

ExercisesSolve each equation. Check your solution.

1. h - 3 = -2 2. m - 8 = -12 3. p - 5 = 15

4. 20 = y - 8 5. k - 0.5 = 2.3 6. w - 1 −

2 = 5 −

8

7. h - 18 = -17 8. -12 = -24 + k 9. j - 0.2 = 1.8

10. b - 40 = -40 11. m - (-12) = 10 12. w - 3 −

2 = 1 −

4

13. x + 12 = 6 14. w + 2 = -13 15. -17 = b + 4

16. k + (-9) = 7 17. -3.2 = � + (-0.2) 18. -

3 −

8 + x =

5 −

8

19. 19 + h = -4 20. -12 = k + 24 21. j + 1.2 = 2.8

22. b + 80 = -80 23. m + (-8) = 2 24. w + 3 −

2 = 5 −

8

Example 2Example 1


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD


Solving One-Step Equations

2-2

PDF Pass


Solve Equations Using Multiplication and Division If each side of an equation is multiplied by the same number, the resulting equation is equivalent to the given one. You can use the property to solve equations involving multiplication and division. To solve equations with multiplication and division, you can also use the Division Property of Equality. If each side of an equation is divided by the same number, the resulting equation is true.

Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc.

Division Property of Equality For any numbers a, b, and c, with c ≠ 0, if a = b, then a − c = b − c .

Solve 3 1 −

2 p = 1 1 −

2 .

3 1 −

2 p = 1 1 −

2 Original equation

7 −

2 p = 3 −

2

2 −

7 (

7 −

2 p

)

= 2 −

7 (

3 −

2 )

Multiply each side by 2 −

7 .

p = 3 −

7 Simplify.

The solution is 3 −

7 .

Solve -5n = 60.

-5n = 60 Original equation

-5n −

-5 = 60 −

-5 Divide each side by -5.

n = -12 Simplify.

The solution is -12.


1. h −

3 = -2 2. 1 −

8 m = 6 3. 1 −

5 p = 3 −

5

4. 5 = y −

12 5. -

1 −

4 k = -2.5 6. -

m −

8 = 5 −

8

7. -1 1 −

2 h = 4 8. -12 = -

3 −

2 k 9.

j −

3 = 2 −

5

10. -3 1 −

3 b = 5 11. 7 −

10 m = 10 12.

p −

5 = -

1 −

4

13. 3h = -42 14. 8m = 16 15. -3t = 51

16. -3r = -24 17. 8k = -64 18. -2m = 16

19. 12h = 4 20. -2.4p = 7.2 21. 0.5j = 5

22. -25 = 5m 23. 6m = 15 24. -1.5p = -75

Example 2Example 1

Rewrite each mixed number as an improper fraction.


Less

on

2-2

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

2-2 Skills PracticeSolving One-Step Equations

PDF Pass


Solve each equation. Check your solution.

1. y - 7 = 8 2. w + 14 = -8

3. p - 4 = 6 4. -13 = 5 + x

5. 98 = b + 34 6. y - 32 = -1

7. n + (-28) = 0 8. y + (-10) = 6

9. -1 = t + (-19) 10. j - (-17) = 36

11. 14 = d + (-10) 12. u + (-5) = -15

13. 11 = -16 + y 14. c - (-3) = 100

15. 47 = w - (-8) 16. x - (-74) = -22

17. 4 - (-h) = 68 18. -56 = 20 - (-j)

19. 12z = 108 20. -7t = 49

21. 18f = -216 22. -22 = 11v

23. -6d = -42 24. 96 = -24a

25. c −

4 = 16 26. a −

16 = 9

27. -84 = d −

3 28. -

d −

7 = -13

29. t −

4 = -13 30. 31 = -

1 −

6 n

31. -6 = 2 −

3 z 32. 2 −

7 q = -4

33. 5 −

9 p = -10 34. a −

10 = 2 −

5


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PracticeSolving One-Step Equations

2-2

PDF Pass



1. d - 8 = 17 2. v + 12 = -5 3. b - 2 = -11

4. -16 = m + 71 5. 29 = a - 76 6. -14 + y = -2

7. 8 - (-n) = 1 8. 78 + r = -15 9. f + (-3) = -9

10. 8j = 96 11. -13z = -39 12. -180 = 15m

13. 243 = 27r 14. y −

9 = -8 15. -

j −

12 = -8

16. a −

15 = 4 −

5 17.

g −

27 = 2 −

9 18.

q −

24 = 1 −

6

Write an equation for each sentence. Then solve the equation.

19. Negative nine times a number equals -117.

20. Negative one eighth of a number is -

3 −

4 .

21. Five sixths of a number is -

5 −

9 .

22. 2.7 times a number equals 8.37.

23. HURRICANES The day after a hurricane, the barometric pressure in a coastal town has risen to 29.7 inches of mercury, which is 2.9 inches of mercury higher than the pressure when the eye of the hurricane passed over.

a. Write an addition equation to represent the situation.

b. What was the barometric pressure when the eye passed over?

24. ROLLER COASTERS Kingda Ka in New Jersey is the tallest and fastest roller coaster in the world. Riders travel at an average speed of 61 feet per second for 3118 feet. They reach a maximum speed of 187 feet per second.

a. If x represents the total time that the roller coaster is in motion for each ride, write an expression to represent the sitation. (Hint: Use the distance formula d = rt.)

b. How long is the roller coaster in motion?


Less

on

2-2

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Word Problem PracticeSolving One-Step Equations

2-2

PDF Pass


1. SUPREME COURT Chief Justice William Rehnquist served on the Supreme Court for 33 years until his death in 2005. Write and solve an equation to determine the year he was confirmed as a justice on the Supreme Court.

2. SALARY In a recent year, the annual salary of the Governor of New York was $179,000. During the same year, the annual salary of the Governor of Tennessee was $94,000 less. Write and solve an equation it to find the annual salary of the Governor of Tennessee in that year.

3. WEATHER On a cold January day, Mavis noticed that the temperature dropped 21 degrees over the course of the day to –9ºC. Write and solve an equation to determine what the temperature was at the beginning of the day.

4. FARMING Mr. Hill’s farm is 126 acres. Mr. Hill’s farm is 1−

4 the size of Mr.

Miller’s farm. How many acres is Mr. Miller’s farm?

5. NAUTICAL On the sea, distances are measured in nautical miles rather than miles.

a. If a boat travels 16 knots in 1 hour, how far will it have traveled in feet? Write and solve an equation.

b. About how fast was the boat traveling in miles per hour? Round your answer to the nearest hundredth.

1 nautical mile = 6080 feet

1 knot = 1 nautical mile −

hour


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment2-2

PDF Pass


Elevator Puzzle José gets on the elevator and rides without pushing any buttons. First, the elevator goes up 4 floors where Bob gets on. Bob goes down 6 floors and gets off. At that same floor Florence gets on and goes up one floor before getting off. The elevator then moves down 8 floors to pick up the Hartt family who ride down 3 floors and get off. Then the elevator goes up one floor, picks up Kris, and goes down 6 floors to the street level where José exits the elevator.

1. Suppose x is your starting point. Write an equation that represents José’s elevator ride.

2. At what floor did José get on the elevator?

Now that you know the starting point of José, the starting point of every other person who rode the elevator can be determined.

3. At what floor did Bob get on the elevator? At what floor did Bob get off?

4. At what floor did Florence get on the elevator? At what floor did Florence get off?

5. At what floor did the Hartt family get on the elevator? At what floor did the Hartt family get off?

6. At what floor did Kris get on the elevator? At what floor did Kris get off?


Less

on

2-3

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Study Guide and InterventionSolving Multi-Step Equations

2-3

PDF Pass


Work Backward Working backward is one of many problem-solving strategies that you can use to solve problems. To work backward, start with the result given at the end of a problem and undo each step to arrive at the beginning number.

A number is divided by 2, and then 8 is subtracted from the quotient. The result is 16. What is the number?Solve the problem by working backward.

The final number is 16. Undo subtracting 8 by adding 8 to get 24. To undo dividing 24 by 2, multiply 24 by 2 to get 48.

The original number is 48.

A bacteria culture doubles each half hour. After 3 hours, there are 6400 bacteria. How many bacteria were there to begin with?Solve the problem by working backward.The bacteria have grown for 3 hours. Since there are 2 one-half hour periods in one hour, in 3 hours there are 6 one-half hour periods. Since the bacteria culture has grown for 6 time periods, it has doubled 6 times. Undo the doubling by halving the number of bacteria 6 times.

6400 × 1 −

2 × 1 −

2 × 1 −

2 × 1 −

2 × 1 −

2 × 1 −

2 = 6400 × 1 −

64

= 100There were 100 bacteria to begin with.

ExercisesSolve each problem by working backward.

1. A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find the number.

2. A number is multiplied by 5, and then 3 is subtracted from the product. The result is 12. Find the number.

3. Eight is subtracted from a number, and then the difference is multiplied by 2. The result is 24. Find the number.

4. Three times a number plus 3 is 24. Find the number.

5. CAR RENTAL Angela rented a car for $29.99 a day plus a one-time insurance cost of $5.00. Her bill was $124.96. For how many days did she rent the car?

6. MONEY Mike withdrew an amount of money from his bank account. He spent one fourth for gasoline and had $90 left. How much money did he withdraw?

Example 2Example 1


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD


Solving Multi-Step Equations

2-3

PDF Pass


Solve Multi-Step Equations To solve equations with more than one operation, often called multi-step equations, undo operations by working backward. Reverse the usual order of operations as you work.

Solve 5x + 3 = 23.

5x + 3 = 23 Original equation

5x + 3 - 3 = 23 - 3 Subtract 3 from each side.

5x = 20 Simplify.

5x −

5 = 20 −

5 Divide each side by 5.

x = 4 Simplify.


1. 5x + 2 = 27 2. 6x + 9 = 27 3. 5x + 16 = 51

4. 14n - 8 = 34 5. 0.6x - 1.5 = 1.8 6. 7 −

8 p - 4 = 10

7. 16 = d - 12 −

14 8. 8 + 3n −

12 = 13 9.

g −

-5 + 3 = -13

10. 4b + 8 −

-2 = 10 11. 0.2x - 8 = -2 12. 3.2y - 1.8 = 3

13. -4 = 7x - (-1)

−

-8 14. 8 = -12 + k −

-4 15. 0 = 10y - 40

Write an equation and solve each problem.

16. Find three consecutive integers whose sum is 96.

17. Find two consecutive odd integers whose sum is 176.

18. Find three consecutive integers whose sum is -93.

Example


Less

on

2-3

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Skills PracticeSolving Multi-Step Equations

2-3

PDF Pass


Solve each problem by working backward.

1. A number is divided by 2, and then the quotient is added to 8. The result is 33.Find the number.

2. Two is subtracted from a number, and then the difference is divided by 3.The result is 30. Find the number.

3. A number is multiplied by 2, and then the product is added to 9. The result is 49.What is the number?

4. ALLOWANCE After Ricardo received his allowance for the week, he went to the mall with some friends. He spent half of his allowance on a new paperback book. Then he bought himself a snack for $1.25. When he arrived home, he had $5.00 left. How much was his allowance?


5. 5x + 3 = 23 6. 4 = 3a - 14 7. 2y + 5 = 19

8. 6 + 5c = -29 9. 8 - 5w = -37 10. 18 - 4v = 42

11. n −

3 - 8 = -2 12. 5 + x −

4 = 1 13. -

h −

3 - 4 = 13

14. -

d −

6 + 12 = -7 15. a −

5 - 2 = 9 16. w −

7 + 3 = -1

17. 3 −

4 q - 7 = 8 18. 2 −

3 g + 6 = -12 19. 5 −

2 z - 8 = -3

20. 4 −

5 m + 2 = 6 21. c - 5 −

4 = 3 22. b + 1 −

3 = 2


23. Twice a number plus four equals 6. What is the number?

24. Sixteen is seven plus three times a number. Find the number.

25. Find two consecutive integers whose sum is 35.

26. Find three consecutive integers whose sum is 36.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PracticeSolving Multi-Step Equations

2-3

PDF Pass


Solve each problem by working backward.

1. Three is added to a number, and then the sum is multiplied by 4. The result is 16. Find the number.

2. A number is divided by 4, and the quotient is added to 3. The result is 24. What is the number?

3. Two is subtracted from a number, and then the difference is multiplied by 5. The result is 30. Find the number.

4. BIRD WATCHING While Michelle sat observing birds at a bird feeder, one fourth of the birds flew away when they were startled by a noise. Two birds left the feeder to go to another stationed a few feet away. Three more birds flew into the branches of a nearby tree. Four birds remained at the feeder. How many birds were at the feeder initially?


5. -12n - 19 = 77 6. 17 + 3f = 14 7. 15t + 4 = 49

8. u −

5 + 6 = 2 9. d −

-4 + 3 = 15 10. b −

3 - 6 = -2

11. 1 −

2 y - 1 −

8 = 7 −

8 12. -32 - 3 −

5 f = -17 13. 8 - 3 −

8 k = -4

14. r + 13 −

12 = 1 15. 15 - a −

3 = -9 16. 3k - 7 −

5 = 16

17. x −

7 - 0.5 = 2.5 18. 2.5g + 0.45 = 0.95 19. 0.4m - 0.7 = 0.22


20. Seven less than four times a number equals 13. What is the number?

21. Find two consecutive odd integers whose sum is 116.

22. Find two consecutive even integers whose sum is 126.

23. Find three consecutive odd integers whose sum is 117.

24. COIN COLLECTING Jung has a total of 92 coins in his coin collection. This is 8 more than three times the number of quarters in the collection. How many quarters does Jung have in his collection?


Less

on

2-3

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Word Problem PracticeSolving Multi-Step Equations

2-3

PDF Pass


1. TEMPERATURE The formula for converting a Fahrenheit temperature to

a Celsius temperature is C =

F - 32º−

1.8 .

Find the equivalent Celsius temperature for 68ºF.

2. HUMAN HEIGHT It is a commonly used guideline that for the average American child, their maximum adult height will be about twice their height at age 2. Suppose that Micah’s adult height fits the following equation a = 2c – 1, where a represents his adult height and c represents his height at age 2. At age 2 Micah was 35 inches tall. What is Micah’s adult height? Write and solve an equation.

3. CHEMISTRY The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. Carbon 14 has a half-life of 5730 years. Suppose

given samples of carbon 14 weigh 5 −

8 of

a pound and 7 −

8 of a pound. What was the

total weight of the samples 11,460 years ago?

4. NUMBER THEORY Write and solve an equation to find three consecutive odd integers whose sum is 3.

5. GEOMETRY A rectangular swimming pool is surrounded by a concrete sidewalk that is 3 feet wide. The dimensions of the rectangle created by the sidewalk are 21 feet by 31 feet.

a. Find the length and width of the pool.

b. Find the area of the pool.

c. Write and solve an equation to find the area of the sidewalk in square feet.

3 ft

31 ft

21 ftpool


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment 2-3

PDF Pass


Consecutive Integer ProblemsMany types of problems and puzzles involve the idea of consecutive integers. Knowing how to represent these integers algebraically can help to solve the problem.

Find four consecutive odd integers whose sum is -80.

An odd integer can be written as 2n + 1, where n is any integer. If 2n + 1 is the first odd integer, then add 2 to get the next largest odd integer, and so on.Now write an equation to solve this problem.(2n + 1) + (2n + 3) + (2n + 5) + (2n + 7) = -80

ExercisesWrite an equation for each problem. Then solve.

1. Complete the solution to the problem in the example.

2. Find three consecutive even integers whose sum is 132.



5. The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.

6. The greater of two consecutive even integers is 6 less than three times the lesser. Find the integers.

7. Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91.

8. Find a set of four consecutive positive integers such that the greatest integer in the set is twice the least integer in the set.

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-4

Study Guide and Intervention Solving Equations with the Variable on Each Side

2-4

PDF Pass


Variables on Each Side To solve an equation with the same variable on each side, first use the Addition or the Subtraction Property of Equality to write an equivalent equation that has the variable on just one side of the equation. Then solve the equation.

Solve 5y - 8 = 3y + 12.

5y - 8 = 3y + 12 5y - 8 - 3y = 3y + 12 - 3y

2y - 8 = 12 2y - 8 + 8 = 12 + 8

2y = 20

2y

−

2 = 20 −

2

y = 10

The solution is 10.

Solve -11 - 3y = 8y + 1.

-11 - 3y = 8y + 1 -11 - 3y + 3y = 8y + 1 + 3y

-11 = 11y + 1 -11 - 1 = 11y + 1 - 1 -12 = 11y

-12 −

11 =

11y −

11

-1 1 −

11 = y

The solution is -1 1 −

11 .


1. 6 - b = 5b + 30 2. 5y - 2y = 3y + 2 3. 5x + 2 = 2x - 10

4. 4n - 8 = 3n + 2 5. 1.2x + 4.3 = 2.1 - x 6. 4.4m + 6.2 = 8.8m - 1.8

7. 1 −

2 b + 4 = 1 −

8 b + 88 8. 3 −

4 k - 5 = 1 −

4 k - 1 9. 8 - 5p = 4p - 1

10. 4b - 8 = 10 - 2b 11. 0.2x - 8 = -2 - x 12. 3y - 1.8 = 3y - 1.8

13. -4 - 3x = 7x - 6 14. 8 + 4k = -10 + k 15. 20 - a = 10a - 2

16. 2 −

3 n + 8 = 1 −

2 n + 2 17. 2 −

5 y - 8 = 9 - 3 −

5 y 18. -4r + 5 = 5 - 4r

19. -4 - 3x = 6x - 6 20. 18 - 4k = -10 -4k 21. 12 + 2y = 10y - 12

Example 1 Example 2


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD


Solving Equations with the Variable on Each Side

2-4

PDF Pass


Grouping Symbols When solving equations that contain grouping symbols, first use the Distributive Property to eliminate grouping symbols. Then solve.

Solve 4(2a - 1) = -10(a - 5).

4(2a - 1) = -10(a - 5) Original equation

8a - 4 = -10a + 50 Distributive Property

8a - 4 + 10a = -10a + 50 + 10a Add 10a to each side.

18a - 4 = 50 Simplify.

18a - 4 + 4 = 50 + 4 Add 4 to each side.

18a = 54 Simplify.

18a −

18 = 54 −


a = 3 Simplify.

The solution is 3.

Exercises Solve each equation. Check your solution.

1. -3(x + 5) = 3(x - 1) 2. 2(7 + 3t) = -t 3. 3(a + 1) - 5 = 3a - 2

4. 75 - 9g = 5(-4 + 2g) 5. 5( f + 2) = 2(3 - f ) 6. 4(p + 3) = 36

7. 18 = 3(2t + 2) 8. 3(d - 8) = 3d 9. 5(p + 3) + 9 = 3( p - 2) + 6

10. 4(b - 2) = 2(5 - b) 11. 1.2(x - 2) = 2 - x 12. 3 + y

−

4 =

-y −

8

13. a - 8 −

12 = 2a + 5 −

3 14. 2(4 + 2k) + 10 = k 15. 2(w - 1) + 4 = 4(w + 1)

16. 6(n - 1) = 2(2n + 4) 17. 2[2 + 3( y - 1)] = 22 18. -4(r + 2) = 4(2 - 4r)

19. -3(x - 8) = 24 20. 4(4 - 4k) = -10 -16k 21. 6(2 - 2y) = 5(2y - 2)

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-4

Skills PracticeSolving Equations with the Variable on Each Side

2-4

PDF Pass


Justify each step.

1. 4k - 3 = 2k + 5

4k - 3 - 2k = 2k + 5 - 2k a.

2k - 3 = 5 b.

2k - 3 + 3 = 5 + 3 c.

2k = 8 d.

2k −

2 = 8 −

2 e.

k = 4 f.

2. 2(8u + 2) = 3(2u - 7)

16u + 4 = 6u - 21 a.

16u + 4 - 6u = 6u - 21 - 6u b.

10u + 4 = -21 c.

10u + 4 - 4 = -21 - 4 d.

10u = -25 e.

10u −

10 = -25 −

10 f.

u = -2.5 g.


3. 2m + 12 = 3m - 31 4. 2h - 8 = h + 17

5. 7a - 3 = 3 - 2a 6. 4n - 12 = 12 - 4n

7. 4x - 9 = 7x + 12 8. -6y - 3 = 3 - 6y

9. 5 + 3r = 5r - 19 10. -9 + 8k = 7 + 4k

11. 8q + 12 = 4(3 + 2q) 12. 3(5j + 2) = 2(3j - 6)

13. 6(-3v + 1) = 5(-2v - 2) 14. -7(2b - 4) = 5(-2b + 6)

15. 3(8 - 3t) = 5(2 + t) 16. 2(3u + 7) = -4(3 - 2u)

17. 8(2f - 2) = 7(3f + 2) 18. 5(-6 - 3d) = 3(8 + 7d)

19. 6(w - 1) = 3(3w + 5) 20. 7(-3y + 2) = 8(3y - 2)

21. 2 −

3 v - 6 = 6 - 2 −

3 v 22. 1 −

2 - 5 −

8 x = 7 −

8 x + 7 −

2


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PracticeSolving Equations with the Variable on Each Side

2-4

PDF Pass



1. 5x - 3 = 13 - 3x 2. -4r - 11 = 4r + 21

3. 1 - m = 6 - 6m 4. 14 + 5n = -4n + 17

5. 1 −

2 k - 3 = 2 -

3 −

4 k 6. 1 −

2 (6 - y) = y

7. 3(-2 - 3x) = -9x - 4 8. 4(4 - w) = 3(2w + 2)

9. 9(4b - 1) = 2(9b + 3) 10. 3(6 + 5y) = 2(-5 + 4y)

11. -5x - 10 = 2 - (x + 4) 12. 6 + 2(3j - 2) = 4(1 + j)

13. 5 −

2 t - t = 3 + 3 −

2 t 14. 1.4f + 1.1 = 8.3 - f

15. 2 −

3 x - 1 −

6 = 1 −

2 x + 5 −

6 16. 2 - 3 −

4 k = 1 −

8 k + 9

17. 1 −

2 (3g - 2) =

g −

2 18. 1 −

3 (n + 1) = 1 −

6 (3n - 5)

19. 1 −

2 (5 - 2h) = h −

2 20. 1 −

9 (2m - 16) = 1 −

3 (2m + 4)

21. 3(d - 8) - 5 = 9(d + 2) + 1 22. 2(a - 8) + 7 = 5(a + 2) - 3a - 19

23. NUMBERS Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number.

24. NUMBERS Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number. What is the number?

25. NUMBER THEORY Tripling the greater of two consecutive even integers gives the same result as subtracting 10 from the lesser even integer. What are the integers?

26. GEOMETRY The formula for the perimeter of a rectangle is P = 2�, + 2w, where � is the length and w is the width. A rectangle has a perimeter of 24 inches. Find its dimensions if its length is 3 inches greater than its width.


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-4

Word Problem PracticeSolving Equations with the Variable on Each Side

2-4

PDF Pass


1. OLYMPICS In the 2010 Winter Olympic Games in Vancouver, Canada, the United States athletes won 1 more than 4 times the number of gold metals won by the French athletes. The United States won 7 more gold metals than the French. Solve the equation 7 + F = 4F + 1 to find the number of gold metals won by the French athletes.

2. AGE Diego’s mother is twice as old as he is. She is also as old as the sum of the ages of Diego and both of his younger twin brothers. The twins are 11 years old. Solve the equation 2d = d + 11 + 11 to find the age of Diego.

3. GEOMETRY Supplementary angles are angles whose measures have a sum of 180º. Complementary angles are angles whose measures have a sum of 90º. Find the measure of an angle whose supplement is 10º more than twice its complement. Let 90 – x equal the degree measure of its complement and 180 – x equal the degree measure of its supplement. Write and solve an equation.

4. NATURE The table shows the current heights and average growth rates of two different species of trees. How long will it take for the two trees to be the same height?

5. NUMBER THEORY Mrs. Simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.

a. Write and solve an equation to find the integers.

b. Does the equation have one solution, no solutions, or is it an identity? Explain.

Tree Species Current Height Annual growth

A 38 inches 4 inches

B 45.5 inches 2.5 inches


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment2-4

PDF Pass


Identities

An equation that is true for every value of the variable is called an identity. When you try to solve an identity, you end up with a statement that is always true. Here is an example.

Solve 8 - (5 - 6x) = 3(1 + 2x).

8 - (5 - 6x) = 3(1 + 2x) Original equation

8 - 5 - (-6x) = 3(1 + 2x) Distributive Property

8 - 5 + 6x = 3 + 6x Distributive Property

3 + 6x = 3 + 6x Add.

Exercises State whether each equation is an identity. If it is not, find its solution.

1. 2(2 - 3x) = 3(3 + x) + 4 2. 5(m + 1) + 6 = 3(4 + m) + (2m - 1)

3. (5t + 9) - (3t - 13) = 2(11 + t) 4. 14 - (6 - 3c) = 4c - c

5. 3y - 2(y + 19) = 9y - 3(9 - y) 6. 3(3h - 1) = 4(h + 3)

7. Use the true equation 3x - 2 = 3x - 2 to create an identity of your own.

8. Use the false equation 1 = 2 to create an equation with no solution.

9. Create an equation whose solution is x = 3.

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-4

Graphing Calculator ActivitySolving Linear Equations

2-4

PDF Pass


Solve 5x - 9 = -3x + 7.

Enter the left side of the equation into Y1 and the right side into the Y2 .

Keystrokes: Y= 5 — 9 ENTER (–) 3 + 7

Graph the equations.

Keystrokes: ZOOM 0 ZOOM 8 ENTER

Use the TRACE key to find the intersection.

Notice the coordinates at the bottom of the screen do not change as you toggle up and down. This indicates a common solution, 2. Substitute 2 into the equation to check the answer. Solve 3 −

4 a + 16 = 2 - 1 −

8 a.

Enter each side of the equation into Y= list.

Keystrokes: Y= ( 3 ÷ 4 ) + 16 ENTER 2 — ( 1 ÷ 8 ) GRAPH .

TRACE to locate the point of intersection at x = -16. So, the solution to the equation is a = -16.

One way to solve a linear equation in one variable is to graph each side of the equation as a separate entity. The intersection of these two graphs identifies the x value for which the equation is true.

[-47, 47] scl:10 by [-31, 31] scl:10

[-47, 47] scl:10 by [-31, 31] scl:10

Exercises Solve each equation.

1. 7(x - 3) = 7 2. 5 - 1 −

2 (x - 6) = 4 3. 1 −

4 (7 + 3z) = - z −

8

4. 28 - 2.2x = 11.6x + 262.6 5. 1.03x - 4 = -2.15x + 8.72 6. c + 1 −

8 - 2 - c −

3 = 5 −

6

7. 6x - 2(x - 3) = 4(x + 1) + 4 8. 5(x - 2) + 2x = 7(x + 4) - 38 9. 8 − x = 2x

Not all equations have integer solutions. Investigate using 2nd [CALC] 5 to solve these equations.

10. 2.4(2x + 3) = -0.1(2x + 3) 11. 9 - 2(5d + 4) = -3(2d - 7) - 10

Example 1

Example 2


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

2-5 Study Guide and Intervention Solving Equations Involving Absolute Value

PDF Pass


Absolute Value Expressions Expressions with absolute values define an upper and lower range in which a value must lie. Expressions involving absolute value can be evaluated using the given value for the variable.

Evaluate ⎪t - 5⎪ - 7 if t = 3.

⎪t - 5⎪ - 7 = ⎪3 - 5⎪ - 7 Replace t with 3.

= ⎪-2⎪ - 7 3 - 5 = -2 = 2 - 7 ⎪-2⎪ = 2 = -5 Simplify.

ExercisesEvaluate each expression if r = -2, n = -3, and t = 3.

1. ⎪8 - t⎪ + 3 2. ⎪t - 3⎪ - 7 3. 5 + ⎪3 - n⎪

4. ⎪r + n⎪ - 7 5. ⎪n - t⎪ + 4 6. - ⎪r + n + t⎪

Evaluate each expression if n = 2, q = -1.5, r = -3, v = -8, w = 4.5, and x = 4.

7. ⎪2q + r

⎪ 8. 10 - ⎪2n + v⎪ 9. ⎪3x - 2w⎪ - q

10. v - ⎪3n + x⎪ 11. 1 + ⎪5q - w

⎪ 12. 2 ⎪3r - v⎪

13. ⎪-2x + 5n⎪ + (n - x) 14. 4w - ⎪2r + v⎪ 15. 3 w - n - 5 q - r

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-5


Solving Equations Involving Absolute Value

2-5

PDF Pass


Absolute Value Equations When solving equations that involve absolute value, there are two cases to consider.Case 1: The value inside the absolute value symbols is positive.Case 2: The value inside the absolute value symbols is negative.

Solve ⎪x + 4⎪ = 1. Then graph the solution set.Write ⎪x + 4⎪ = 1 as x + 4 = 1 or x + 4 = -1.

x + 4 = 1 or x + 4 = -1 x + 4 - 4 = 1 - 4 x + 4 - 4 = -1 - 4 x = -3 x = -5

The solution set is {-5, -3}.The graph is shown below.

-8 -7 -6 -5 -4 -3 -2 -1 0

Write an equation involving absolute value for the graph.

Find the point that is the same distance from -2 as it is from 4.

The distance from 1 to -2 is 3 units. The distance from 1 to 4 is 3 units.So, ⎪x - 1⎪ = 3.

-3 -2 -1 0 1 2 3 4 5

10-1-2-3 2 3

3 units 3 units

4 5

ExercisesSolve each equation. Then graph the solution set.

1. ⎪

y⎪

= 3 2. ⎪x - 4⎪ = 4 3. ⎪y + 3

⎪ = 2

-3-4 -2 -1 0 1 2 3 4 0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1 0

4. ⎪b + 2 ⎪ = 3 5. ⎪w - 2 ⎪ = 5 6. ⎪t + 2 ⎪ = 4

-6 -5 -4 -3 -2 -1 0 1 2 -8 -6 -4 -2 0 2 4 6 8 -8 -6 -4 -2 0 2 4 6 8

7. ⎪2x⎪ = 8 8. ⎪5y - 2

⎪ = 7 9.

⎪p - 0.2

⎪ = 0.5

-3-4 -2 -1 0 1 2 3 4 -3-4 -2 -1 0 1 2 3 4 -0.8 -0.4 0 0.4 0.8

10. ⎪d - 100⎪ = 50 11. ⎪2x - 1⎪ = 11 12. ⎪

3x + 1 −

2 ⎪

= 6

50 100 150 200 -4-6 -2 0 2 4 6 8 10 -2-3 -1 0 1 2 3 4 5

Write an equation involving absolute value for each graph.

13. 0-2-4-6-8 2 4 6 8

14. -3-4 -2 -1 0 1 2 3 4

15. -3-4-5-6-7 -2 -1 0 1

Example 1 Example 2


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Skills PracticeSolving Equations Involving Absolute Value

2-5

PDF 2nd


Evaluate each expression if a = 2, b = -3, and c = -4.

1. ⎪a - 5⎪ - 1 2. ⎪b + 1⎪ + 8

3. 5 - ⎪c + 1⎪ 4. ⎪a + b⎪ - c

Solve each equation. Then graph the solution set.

5. ⎪w + 1⎪ = 5 6. ⎪c - 3⎪ = 1

7. ⎪n + 2⎪ = 1 8. ⎪t + 6⎪ = 4

9. ⎪w - 2⎪ = 2 10. ⎪k - 5⎪ = 4


11. -5 -4 -3 -2 -1 0 1 2 3 4 5

12.

13. 14.

-2 -1-4-5-6 -3 0 1 2 3 4-8 -7-10 -9 -6 -5 -4 -3 -2 -1 0

0 1 2 3 4 5 6 7 8 9 10

-2-3-4-5-6-7 -1 0 1 2 3

-2-3-4-5 -1 0 1 2 3 4 5 -2-3-4-5 -1 0 1 2 3 4 5

-3-4-5-6 -2 -1 0 1 2 3 4 -3 -1 0 1 2 3 4 5 6-2 7

-3-4 -2 -1 0 1 2 3 4 5 6


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-5

PracticeSolving Equations Involving Absolute Value

2-5

PDF Pass


Evaluate each expression if x = -1, y = 3, and z = -4.

1. 16 - ⎪2z + 1⎪ 2. ⎪

x - y⎪

+ 4

3. ⎪-3y + z

⎪ - x 4. 3 ⎪z - x⎪ +

⎪2 - y

⎪

Solve each equation. Then graph the solution set.

5. |2z - 9| = 1 6. |3 - 2r| = 7

-5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5

7. |3t + 6| = 9 8. |2 g - 5| = 9

-5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1 0 1 2 3 4 5 6 7 8


9. 1 2 3 4 5 6 7 8 9 10 11

10. -2-3-4-5-6-7-8 -1 0 1 2

11. -2-3-4-5-6-7-8 -1 0 1 2

12. -2-3 -1 0 1 2 3 4 5 6 7

13. FITNESS Taisha uses the elliptical cross-trainer at the gym. Her general goal is to burn 280 Calories per workout, but she varies by as much as 25 Calories from this amount on any given day. Write and solve an equation to find the maximum and minimum number of Calories Taisha burns on the cross-trainer.

14. TEMPERATURE A thermometer is guaranteed to give a temperature no more than 1.2°F from the actual temperature. If the thermometer reads 28°F, write and solve an equation to find the maximum and minimum temperatures it could be.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Word Problem PracticeSolving Open Sentences Involving Absolute Value

2-5

PDF 2nd


1. ENGINEERING Tolerance in engineering is an allowance made for imperfections in a manufactured object. The manufacturer of an oven specifies a temperature tolerance of ±15ºF. This means that the temperature inside the oven will be within 15ºF of the temperature that it is set on. Write an absolute value expression to represent the maximum and minimum temperatures inside the oven when the thermostat is set on 400ºF.

2. AVIATION The circle graph shows the results of a survey that asked 4300 students ages 7 to 18 what they thought would be the most important benefit of air travel in the future. There are about 40 million students in the United States. If the margin of error is ±3%, what is the range of the number of students ages 7 to 18 who would likely say that “finding new resources for Earth” is the most important benefit of future flight?

Source: The World Almanac

3. COLLEGE A certain scholarship and student loan fund uses a formula to determine whether or not a student qualifies for college funding. The formula is ⎪3k + 6⎪ = 15, where k is a need score determined by an interview. What are the possible need scores?

4. STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one deviation of the mean have IQ scores that are 15 points higher or lower than the mean.

a. Write an absolute value equation tofind the maximum and minimum test scores within one standard deviation if the mean was 80 and the standard deviation was 12.

b. What is the range of Wechsler IQ test scores ±3 standard deviations from the mean?

43%

26%

10%

21%

Finding new resourcesfor Earth

The Next Frontier for Flight

Scientificexperimentsin space

Flying fasterfrom onecontinentto another

Exploring other planetsin our solar system

for signs of life


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-5

Enrichment2-5

PDF Pass


Precision of MeasurementThe precision of a measurement depends both on your accuracy in measuring and the number of divisions on the ruler you use. Suppose you measured a length of wood to the nearest one-eighth of an inch and got a length of 6 5 −

8 in.

The drawing shows that the actual measurement lies somewhere

between 6 9−16

in. and 6 11−

16 in. This measurement can be written using

the symbol ±, which is read plus or minus.

6 5−8

±

1−

16 in.

In this example, 1−16

in. is the absolute error. The absolute error is

one-half the smallest unit used in a measurement.

Find the maximum and minimum lengths for each measurement.

1. 3 1 −

2 ± 1 −

4 in. 2. 9.78 ± 0.005 cm 3. 2.4 ± 0.05 g

4. 28 ± 1 −

2 ft 5. 15 ± 0.5 cm 6. 11 −

16 ± 1 −

64 in.

For each measurement, give the smallest unit used and the absolute error.

7. The actual measurement is between 12.5 cm and 13.5 cm.

8. The actual measurement is between 12 1 −

8 in. and 12 3 −

8 in.

9. The actual measurement is between 56 1 −

2 in. and 57 1 −

2 in.

10. The actual measurement is between 23.05 mm and 23.15 mm.

5 6 7 8

6 5–8


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Study Guide and InterventionRatios and Proportions

2-6

PDF Pass


Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio of x to y can be expressed as x to y, x:y or x − y . Ratios are usually expressed in simplest form. An equation stating that two ratios are equal is called a proportion. To determine whether two ratios form a proportion, express both ratios in simplest form or check cross products.

Determine whether the

ratios 24 −

36 and 12 −

18 are equivalent ratios.

Write yes or no. Justify your answer.

24 −

36 = 2 −

3 when expressed in simplest form.

12 −

18 = 2 −

3 when expressed in simplest form.

The ratios 24 −

36 and 12 −

18 form a proportion

because they are equal when expressed in simplest form.

Use cross products to

determine whether 10 −

18 and 25 −

45 form a

proportion.

10 −

18 � 25 −

45 Write the proportion.

10(45) � 18(25) Cross products

450 = 450 Simplify.

The cross products are equal, so 10 −

18 = 25 −

45 .

Since the ratios are equal, they form a proportion.

Exercises

Determine whether each pair of ratios are equivalent ratios. Write yes or no.

1. 1 −

2 , 16 −

32 2. 5 −

8 , 10 −

15 3. 10 −

20 , 25 −

49

4. 25 −

36 , 15 −

20 5. 12 −

32 , 3 −

16 6. 4 −

9 , 12 −

27

7. 0.1 −

2 , 5 −

100 8. 15 −

20 , 9 −

12 9. 14 −

12 , 20 −

30

10. 2 −

3 , 20 −

30 11. 5 −

9 , 25 −

45 12. 72 −

64 , 9 −

8

13. 5 −

5 , 30 −

20 14. 18 −

24 , 50 −

75 15. 100 −

75 , 44 −

33

16. 0.05 −

1 , 1 −

20 17. 1.5 −

2 , 6 −

8 18. 0.1 −

0.2 , 0.45 −

0.9

Example 1 Example 2


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-6


Ratios and Proportions

2-6

PDF Pass


Solve Proportions If a proportion involves a variable, you can use cross products to solvethe proportion. In the proportion x −

5 = 10 −

13 , x and 13 are called extremes. They are the first

and last terms of the proportion. 5 and 10 are called means. They are the middle terms of the proportion. In a proportion, the product of the extremes is equal to the product of the means.

Solve x −

5 = 10 −

13 .

x −

5 = 10 −

13 Original proportion

13(x) = 5(10) Cross products

13x = 50 Simplify.

13x −

13 = 50 −


x = 3 11 −

13 Simplify.

ExercisesSolve each proportion. If necessary, round to the nearest hundredth.

1. -3 − x = 2 −

8 2. 1 − t = 5 −

3 3. 0.1 −

2 = 0.5 − x

4. x + 1 −

4 = 3 −

4 5. 4 −

6 = 8 − x 6. x −

21 = 3 −

63

7. 9 −

y + 1 = 18 −

54 8. 3 −

d = 18 −

3 9. 5 −

8 =

p −

24

10. 4 −

b - 2 = 4 −

12 11. 1.5 − x = 12 − x 12.

3 + y −

4 =

-y −

8

13. a - 18 −

12 = 15 −

3 14. 12 −

k = 24 −

k 15. 2 + w −

6 = 12 −

9

Use a proportion to solve each problem.

16. MODELS To make a model of the Guadeloupe River bed, Hermie used 1 inch of clay for 5 miles of the river’s actual length. His model river was 50 inches long. How long is the Guadeloupe River?

17. EDUCATION Josh finished 24 math problems in one hour. At that rate, how many hours will it take him to complete 72 problems?

Means-Extremes Property of ProportionsFor any numbers a, b, c, and d, if a −

b = c −

d , then

ad = bc.

Example


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Skills PracticeRatios and Proportions

2-6

PDF Pass



1. 4 −

5 , 20 −

25 2. 5 −

9 , 7 −

11

3. 6 −

7 , 24 −

28 4. 8 −

9 , 72 −

81

5. 7 −

16 , 42 −

90 6. 13 −

19 , 26 −

38

7. 3 −

14 , 21 −

98 8. 12 −

17 , 50 −

85

Solve each proportion. If necessary, round to the nearest hundredth.

9. 1 − a = 2 −

14 10. 5 −

b = 3 −

9

11. 9 − g = 15 −

10 12. 3 − a = 1 −

6

13. 6 − z = 3 −

5 14. 5 −

f = 35 −

21

15. 12 −

7 = 36 − m 16. 6 −

23 =

y −

69

17. 42 −

56 = 6 −

f 18. 7 −

b = 1 −

9

19. 10 −

14 = 30 − m 20. 11 −

15 = n −

60

21. 9 − c = 27 −

39 22. 5 −

12 = 20 − g

23. 4 −

21 =

y −

84 24. 22 − x = 11 −

30

25. BOATING Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate,how many gallons of gasoline will the boat use in 10 hours?


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-6

PracticeRatios and Proportions

2-6

PDF Pass



1. 7 −

6 , 52 −

48 2. 3 −

11 , 15 −

66 3. 18 −

24 , 36 −

48

4. 12 −

11 , 108 −

99 5. 8 −

9 , 72 −

81 6. 1.5 −

9 , 1 −

6

7. 3.4 −

5.2 , 7.14 −

10.92 8. 1.7 −

1.2 , 2.9 −

2.4 9. 7.6 −

1.8 , 3.9 −

0.9

Solve each proportion. If necessary, round to the nearest hundredth.

10. 5 − a = 30 −

54 11. v −

46 = 34 −

23 12. 40 −

56 = k −

7

13. 28 −

49 = 4 −

w 14. 3 − u = 27 −

162 15.

y −

3 = 48 −

9

16. 2 − y = 10 −

60 17. 5 −

11 = 35 −

x 18. 3 −

51 = z −

17

19. 6 −

61 = 12 −

h 20.

g −

16 = 6 −

4 21. 14 −

49 = 2 −

a

22. 7 −

9 = 8 − t 23. 3 − q = 5 −

6 24. m −

6 = 5 −

8

25. v −

0.23 = 7 −

1.61 26. 3 −

0.72 = 12 −

b 27. 6 − n = 3 −

0.51

28. 7 −

a - 4 = 14 −

6 29. 3 −

12 = 2 −

y + 6 30. m - 1 −

8 = 2 −

4

31. 5 −

12 = x + 1 −

4 32. r + 2 −

7 = 5 −

7 33. 3 −

7 = x - 2 −

6

34. PAINTING Ysidra paints a room that has 400 square feet of wall space in 2 1 −

2 hours.

At this rate, how long will it take her to paint a room that has 720 square feet of wall space?

35. VACATION PLANS Walker is planning a summer vacation. He wants to visit Petrified National Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a large meteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about

1 1 −

2 inches apart. What is the distance between Petrified National Forest and Meteor

Crater?


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Word Problem PracticeRatios and Proportions

2-6

PDF Pass


1. WATER A dripping faucet wastes 3 cups of water every 24 hours. How much water is wasted in a week?

2. GASOLINE In November 2010 the average price of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the price for 16 gallons of gas?

3. SHOPPING Stevenson’s Market is selling 3 packs of toothpicks for $0.87. How much will 10 packs of toothpicks cost at this price? Round your answer to the nearest cent.

4. BUILDINGS Willis Tower in Chicago is 1450 feet tall. The John Hancock Center in Chicago is 1127 feet tall. Suppose you are asked to build a small-scale replica of each. If you make the Willis Tower 3 meters tall, what would be the approximate height of the John Hancock replica? Round your answer to the nearest hundredth.

5. MAPS A map of Waco, Texas and neighboring towns is shown below.

a. Use a metric ruler to measure the distances between Robinson and Neale on the map.

b. Using the scale of the map, find the approximate actual distance by air (not by roads), between Robinson and Neale.

c. Approximately how many square miles are shown on this map?

0 5 mi

6

484

84

35

TexasRoss

Waco

Neale

Robinson

Bellmead

Hewitt

China Spring


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-6

Enrichment2-6

PDF Pass


Angles of a TriangleIn geometry, many statements about physical space are proven to be true. Such statements are called theorems. Here are two examples of geometric theorems.

a. The sum of the measures of the angles of a triangle is 180°.

b. If two sides of a triangle have equal measure, then the two angles opposite those sides also have equal measure.

For each of the triangles, write an equation and then solve for x. (A tick mark on two or more sides of a triangle indicates that the sides have equal measure.)

1. 70°

50°x °

2.

90° 45°

x °

3.

90° x

4. (x + 30)°

x °(5x + 10)°

5. 5x °

2x ° x

6.

90°

4x °

5x °

7.

(x - 15)°

3x °

(x + 30)°

8.

40°

x °

9.

x °

10.

x °2x °

30°

11. Two angles of a triangle have the same 12. The measure of one angle of a triangle is measure. The sum of the measures of twice the measure of a second angle. The these angles is one-half the measure of measure of the third angle is 12 less than the third angle. Find the measures of the sum of the other two. Find the the angles of the triangle. measures of the angles of the triangle.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Study Guide and InterventionPercent of Change

2-7

PDF Pass


Percent of Change When an increase or decrease in an amount is expressed as a percent, the percent is called the percent of change. If the new number is greater than the original number, the percent of change is a percent of increase. If the new number is less than the original number, the percent of change is the percent of decrease.

Find the percent of increase. original: 48

new: 60First, subtract to find the amount of increase. The amount of increase is 60 - 48 = 12.Then find the percent of increase by using the original number, 48, as the base.

12 −

48 = r −

100 Percent proportion

12(100) = 48(r) Cross products

1200 = 48r Simplify.

1200 −

48 = 48r −


25 = r Simplify.

The percent of increase is 25%.

Find the percent of decrease. original: 30

new: 22First, subtract to find the amount of decrease. The amount of decrease is 30 - 22 = 8.Then find the percent of decrease by using the original number, 30, as the base.

8 −

30 = r −

100 Percent proportion

8(100) = 30(r) Cross products

800 = 30r Simplify.

800 −

30 = 30r −


26 2 −

3 = r Simplify.

The percent of decrease is 26 2 −

3 %, or

about 27%.

ExercisesState whether each percent of change is a percent of increase or a percent of decrease. Then find each percent of change. Round to the nearest whole percent.

1. original: 50 2. original: 90 3. original: 45new: 80 new: 100 new: 20

4. original: 77.5 5. original: 140 6. original: 135new: 62 new: 150 new: 90

7. original: 120 8. original: 90 9. original: 27.5new: 180 new: 270 new: 25

10. original: 84 11. original: 12.5 12. original: 250new: 98 new: 10 new: 500

Example 2Example 1


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-7

2-7 Study Guide and Intervention (continued)

Percent of Change

PDF Pass


Solve Problems Discounted prices and prices including tax are applications of percent of change. Discount is the amount by which the regular price of an item is reduced. Thus, the discounted price is an example of percent of decrease. Sales tax is an amount that is added to the cost of an item, so the price including tax is an example of percent of increase.

SALES A coat is on sale for 25% off the original price. If the original price of the coat is $75, what is the discounted price?

The discount is 25% of the original price.

25% of $75 = 0.25 × 75 25% = 0.25

= 18.75 Use a calculator.

Subtract $18.75 from the original price.

$75 - $18.75 = $56.25

The discounted price of the coat is $56.25.

Exercises Find the total price of each item.

1. Shirt: $24.00 2. CD player: $142.00 3. Celebrity calendar: $10.95Sales tax: 4% Sales tax: 5.5% Sales tax: 7.5%

Find the discounted price of each item.

4. Compact disc: $16 5. Two concert tickets: $28 6. Airline ticket: $248.00Discount: 15% Student discount: 28% Superair discount: 33%

7. VIDEOS The original selling price of a new sports video was $65.00. Due to the demand the price was increased to $87.75. What was the percent of increase over the original price?

8. SCHOOL A high school paper increased its sales by 75% when it ran an issue featuring a contest to win a class party. Before the contest issue, 10% of the school’s 800 students bought the paper. How many students bought the contest issue?

9. BASEBALL Baseball tickets cost $15 for general admission or $20 for box seats. The sales tax on each ticket is 8%. What is the final cost of each type of ticket?

Example


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Skills PracticePercent of Change

2-7

PDF Pass


State whether each percent of change is a percent of increase or a percent of decrease. Then find each percent of change. Round to the nearest whole percent.

1. original: 25 2. original: 50new: 10 new: 75




Find the total price of each item.

9. dress: $69.00 10. binder: $14.50tax: 5% tax: 7%

11. hardcover book: $28.95 12. groceries: $47.52tax: 6% tax: 3%

13. filler paper: $6.00 14. shoes: $65.00tax: 6.5% tax: 4%

15. basketball: $17.00 16. concert tickets: $48.00tax: 6% tax: 7.5%


17. backpack: $56.25 18. monitor: $150.00discount: 20% discount: 50%

19. CD: $15.99 20. shirt: $25.50discount: 20% discount: 40%

21. sleeping bag: $125 22. coffee maker: $102.00discount: 25% discount: 45%


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-7

2-7 PracticePercent of Change

PDF Pass


State whether each percent of change is a percent of increase or a percent of decrease. Then find each percent of change. Round to the nearest whole percent.



7. original: 15 8. original: 98.6 9. original: 58.8new: 35.5 new: 64 new: 65.7

Find the total price of each item.

10. concrete blocks: $95.00 11. crib: $240.00 12. jacket: $125.00tax: 6% tax: 6.5% tax: 5.5%

13. class ring: $325.00 14. blanket: $24.99 15. kite: $18.90tax: 6% tax: 7% tax: 5%


16. dry cleaning: $25.00 17. computer game: $49.99 18. luggage: $185.00discount: 15% discount: 25% discount: 30%

19. stationery: $12.95 20. prescription glasses: $149 21. pair of shorts: $24.99 discount: 10% discount: 20% discount: 45%

Find the final price of each item.

22. television: $375.00 23. DVD player: $269.00 24. printer: $255.00discount: 25% discount: 20% discount: 30%tax: 6% tax: 7% tax: 5.5%

25. INVESTMENTS The price per share of a stock decreased from $90 per share to $36 per share. By what percent did the price of the stock decrease?

26. HEATING COSTS Customers of a utility company received notices in their monthly bills that heating costs for the average customer had increased 125% over last year because of an unusually severe winter. In January of last year, the Garcia’s paid $120 for heating. What should they expect to pay this January if their bill increased by 125%?


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Word Problem PracticePercent of Change

2-7

PDF Pass


1. SPORTS A regulation girls’ fast pitch softball diamond has bases that are 60 feet apart. A regulation professional baseball diamond has bases that are 50% farther apart. Label the distance between the bases on the regulation baseball diamond diagram.

2. SALES TAX Olivia purchases a DVD movie priced at $21.99. The sales tax is 6.5%. What is the total price of the movie, including tax?

3. EDUCATION The ACT is a college entrance exam taken by high school students. The maximum score that can be earned is 36. The average score in the United States was 21.2 during a recent year. The average score for Vermont students that year was 7.5% higher than the national average. What was the average ACT score for Vermont students? Round your answer to the nearest tenth.

4. CARS Mr. Thompson plans to purchase a used car priced at $8400. He will receive a 15% employee discount and then will have to pay a 5.5% sales tax. What will be the final price of the car?

5. MUSIC The table below shows the total number of CDs, downloaded singles, and music videos sold in 2004, 2006, and 2008.

Source: Recording Industry Association of America

a. Find the percent of change in the number of units sold between 2004 and 2006 and between 2006 and 2008 for each format. Round your answers to the nearest tenth.

b. Tell whether each percent of change in part a is a percent of increase or a percent of decrease.

c. Did these trends change from 2004 to 2008? Explain.

Sales of Recorded Music and Music Videos

(millions of units)

Format 2004 2006 2008

CD 767.0 614.9 368.4

Downloaded 139.4 586.4 1042.7

Video 32.8 23.1 20.8


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-7

Enrichment 2-7

PDF Pass


Using Percent

Use what you have learned about percent to solve each problem.A TV movie had a “rating” of 15 and a 25 “share.” The rating is the percentage of the nation’s total TV households that were tuned in to this show. The share is the percentage of homes with TVs turned on that were tuned to the movie. How many TV households had their TVs turned off at this time? To find out, let T = the number of TV households

and x = the number of TV households with the TV off. Then T - x = the number of TV households with the TV on.

Since 0.15T and 0.25(T - x) both represent the number of households tuned to the movie,

0.15T = 0.25(T - x) 0.15T = 0.25T - 0.25x.

Solve for x. 0.25x = 0.10T

x = 0.10T −

0.25 or 0.40T

Forty percent of the TV households had their TVs off when the movie was aired.

Answer each question.

1. During that same week, a sports broadcast had a rating of 22.1 and a 43 share. Show that the percent of TV households with their TVs off was about 48.6%.

2. Find the percent of TV households with their TVs turned off during a show with a rating of 18.9 and a 29 share.

3. Show that if T is the number of TV households, r is the rating, and s is the

share, then the number of TV households with the TV off is (s - r)T − s .

4. If the fraction of TV households with no TV on is s - r − s then show that the

fraction of TV households with TVs on is r − s .

5. Find the percent of TV households with TVs on during the most watched serial program in history: the last episode of M*A*S*H, which had a 60.3 rating and a 77 share.

6. A local station now has a 2 share. Each share is worth $50,000 in advertising revenue per month. The station is thinking of going commercial free for the three months of summer to gain more listeners. What would its new share have to be for the last 4 months of the year to make more money for the year than it would have made had it not gone commercial free?


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Spreadsheet ActivityDiscounts

2-7

PDF Pass


Exercises 1. For the second week of the sale, the Electronics Warehouse manager is

changing the discounts to 20%, 30%, 45%, and 75% off. Use a spreadsheet to create a new discount price list for the software.

2. How should the spreadsheet be altered if the manager wished to show the final prices of the software including the 6% sales tax for their area?

Electronics Warehouse is having a software clearance sale. The manager is making a discounted price list to distribute to customers as they shop. Different tables will have software that is discounted by a different percent. Use a spreadsheet to show the discounted price of software that is originally priced $5.99, $7.99, $9.99, $15.99, $19.99, $23.99, $27.99, $29.99, $33.99, and $35.99. Compute discounted prices for software that is 10%, 15%, 25%, and 50% off.

If an item is on sale for 10% off, that means that discounted price is (1 - 0.1) or 0.9 times the original price. Use this pattern to complete the spreadsheet.

Step 1 Use Column A of the spreadsheet for the original prices.

Step 2 Columns B through E contain the formulas for the discounted prices.

Step 3 Because these are prices, the numbers must be rounded to 2 digits. You can program the spreadsheet to list the information as dollars and cents by choosing currency from the number menu when you format the cells.

Discounts.xlsA

1

34567891011

2

B C D E

12Sheet 1 Sheet 2 Sheet 3

The formula incell C11 is 0.85*A11

The formula incell E6 is 0.5*A6

Original price 10 % off 15 % off 25 % off 50 % off

$5.99$7.99$9.99

$15.99$19.99$23.99$27.99$29.99$33.99$35.99

$5.39$7.19$8.99

$14.39$17.99$21.59$25.19$26.99$30.59$32.39

$5.09$8.79$8.49

$13.59$16.99$20.39$23.79$25.49$28.89$30.59

$3.00$4.00$5.00$8.00

$10.00$12.00$14.00$15.00$17.00$18.00

$4.49$5.99$7.49

$11.99$14.99$17.99$20.99$22.49$25.49$26.99


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-8

2-8 Study Guide and InterventionLiteral Equations and Dimensional Analysis

PDF Pass


Solve for Variables Sometimes you may want to solve an equation such as V = �wh for one of its variables. For example, if you know the values of V, w, and h, then the equation

� = V −

wh is more useful for finding the value of �. If an equation that contains more than one

variable is to be solved for a specific variable, use the properties of equality to isolate the specified variable on one side of the equation.

Solve 2x - 4y = 8, for y.

2x - 4y = 8 2x - 4y - 2x = 8 - 2x

-4y = 8 - 2x

-4y −

-4 = 8 - 2x −

-4

y = 8 - 2x −

-4 or 2x - 8 −

4

The value of y is 2x - 8 −

4 .

Solve 3m - n = km - 8, for m.

3m - n = km - 8 3m - n - km = km - 8 - km 3m - n - km = - 8

3m - n - km + n = - 8 + n 3m - km = -8 + n m(3 - k) = -8 + n

m(3 - k) −

3 -k = -8 + n −

3 - k

m = -8 + n −

3 - k or n - 8 −

3 - k

The value of m is n - 8 −

3 - k . Since division by 0 is

undefined, 3 - k ≠ 0, or k ≠ 3.

Exercises Solve each equation or formula for the variable indicated.

1. ax - b = c, for x 2. 15x + 1 = y, for x 3. (x + f ) + 2 = j, for x

4. xy + w = 9, for y 5. x(4 - k) = p, for k 6. 7x + 3y = m, for y

7. 4(r + 3) = t, for r 8. 2x + b = w, for x 9. x(1 + y) = z, for x

10. 16w + 4x = y, for x 11. d = rt, for r 12. A = h(a + b) −

2 , for h

13. C = 5 −

9 (F - 32), for F 14. P = 2� + 2w, for w 15. A = �w, for �

Example 2Example 1


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD


Literal Equations and Dimensional Analysis

2-8

PDF Pass


Use Formulas Many real-world problems require the use of formulas. Sometimes solving a formula for a specified variable will help solve the problem.

The formula C = πd represents the circumference of a circle, or the distance around the circle, where d is the diameter. If an airplane could fly around Earth at the equator without stopping, it would have traveled about 24,900 miles. Find the diameter of Earth.

C = πd Given formula

d = C −

π

Solve for d.

d = 24,900

−

3.14 Use π = 3.14.

d ≈ 7930 Simplify.

The diameter of Earth is about 7930 miles.

Exercises 1. GEOMETRY The volume of a cylinder V is given by the formula V = πr2h, where r is

the radius and h is the height.

a. Solve the formula for h.

b. Find the height of a cylinder with volume 2500π cubic feet and radius 10 feet.

2. WATER PRESSURE The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.

a. Solve the formula for d.

b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.

3. GRAPHS The equation of a line containing the points (a, 0) and (0, b) is given by the

formula x − a + y −

b = 1.

a. Solve the equation for y.

b. Suppose the line contains the points (4, 0), and (0, -2). If x = 3, find y.

4. GEOMETRY The surface area of a rectangular solid is given by the formula x = 2�w + 2�h + 2wh, where � = length, w = width, and h = height.


b. The surface area of a rectangular solid with length 6 centimeters and width 3 centimeters is 72 square centimeters. Find the height.

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-8

Skills PracticeLiteral Equations and Dimensional Analysis

2-8

PDF 2nd


Solve each equation or formula for the variable indicated.

1. 7t = x, for t 2. r = wp, for p

3. q - r = r, for r 4. 4m - t = m, for m

5. 7a - b = 15a, for a 6. -5c + d = 2c, for c

7. x - 2y = 1, for y 8. d + 3n = 1, for n

9. 7f + g = 5, for f 10. ax - c = b, for x

11. rt - 2n = y, for t 12. bc + 3g = 2k, for c

13. kn + 4f = 9v, for n 14. 8c + 6j = 5p, for c

15. x - c −

2 = d, for x 16. x - c −

2 = d, for c

17. p + 9

−

5 = r, for p 18. b - 4z −

7 = a, for b

19. The volume of a box V is given by the formula V = ℓwh, where ℓ is the length, w is the width, and h is the height.


b. What is the height of a box with a volume of 50 cubic meters, length of 10 meters, and width of 2 meters?

20. Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S. = 0.678 euros, find the cost of the souvenirs in United States dollars. Round to the nearest cent.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PracticeLiteral Equations and Dimensional Analysis

2-8

PDF 2nd


Solve each equation or formula for the variable indicated.

1. d = rt, for r 2. 6w - y = 2z, for w

3. mx + 4y = 3t, for x 4. 9s - 5g = -4u, for s

5. ab + 3c = 2x, for b 6. 2p = kx - t, for x

7. 2 −

3 m + a = a + r, for m 8. 2 −

5 h + g = d, for h

9. 2 −

3 y + v = x, for y 10. 3 −

4 a - q = k, for a

11. rx + 9 −

5 = h, for x 12. 3b - 4 −

2 = c, for b

13. 2w - y = 7w - 2, for w 14. 3� + y = 5 + 5�, for �

15. ELECTRICITY The formula for Ohm’s Law is E = IR, where E represents voltage measured in volts, I represents current measured in amperes, and R represents resistance measured in ohms.

a. Solve the formula for R.

b. Suppose a current of 0.25 ampere flows through a resistor connected to a 12-volt battery. What is the resistance in the circuit?

16. MOTION In uniform circular motion, the speed v of a point on the edge of a spinning disk is v = 2π

−

t r, where r is the radius of the disk and t is the time it takes the point to

travel once around the circle.

a. Solve the formula for r.

b. Suppose a merry-go-round is spinning once every 3 seconds. If a point on the outside edge has a speed of 12.56 feet per second, what is the radius of the merry-go-round? (Use 3.14 for π.)

17. HIGHWAYS Interstate 90 is the longest interstate highway in the United States, connecting the cities of Seattle, Washington and Boston, Massachusetts. The interstate is 4,987,000 meters in length. If 1 mile = 1.609 kilometers, how many miles long is Interstate 90?


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-8

Word Problem PracticeLiteral Equations and Dimensional Analysis

2-8

PDF Pass


1. INTEREST Simple interest that you may earn on money in a savings account can be calculated with the formula I = prt. I is the amount of interest earned, p is the principal or initial amount invested, r is the interest rate, and t is the amount of time the money is invested for. Solve the formula for p.

2. DISTANCE The distance d a car can travel is found by multiplying its rate of speed r by the amount of time t that it took to travel the distance. If a car has already traveled 5 miles, the total distance d is found by the formula d = rt + 5 . Solve the formula for r.

3. ENVIRONMENT The United States released 5.877 billion metric tons of carbon dioxide into the environment through the burning of fossil fuels in a recent year. If 1 trillion pounds = 0.4536 billion metric tons, how many trillions of pounds of carbon dioxide did the United States release in that year?

4. PHYSICS The pressure exerted on an object is calculated by the formula

P = F−A

, where P is the pressure, F is the force, and A is the surface area of the object. Water shooting from a hose has a pressure of 75 pounds per square inch (psi). Suppose the surface area covered by the direct hose spray is 0.442 square inch. Solve the equation for F and find the force of the spray.

5. GEOMETRY The regular octagon is divided into 8 congruent triangles. Each triangle has an area of 21.7 square centimeters. The perimeter of the octagon is 48 centimeters.

a. What is the length of each side of the octagon?

b. Solve the area of a triangle formula for h.

c. What is the height of each triangle? Round to the nearest tenth.

h


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment2-8

PDF Pass


Compound InterestIn most banks, interest on savings accounts is compounded at set time periods such as three or six months. At the end of each period, the bank adds the interest earned to the account. During the next period, the bank pays interest on all the money in the bank, including interest. In this way, the account earns interest on interest.Suppose Ms. Tanner has $1000 in an account that is compounded quarterly at 5%. Find the balance after the first two quarters.Use I = prt to find the interest earned in the first quarter if p = 1000

and r = 5%. Why is t equal to 1 −

4 ?

First quarter: I = 1000 × 0.05 × 1 −

4

I = 12.50

The interest, $12.50, earned in the first quarter is added to $1000. The principal becomes $1012.50.

Second quarter: I = 1012.50 × 0.05 × 1 −

4

I = 12.65625

The interest in the second quarter is $12.66.

The balance after two quarters is $1012.50 + 12.66 or $1025.16.

Answer each of the following questions.

1. How much interest is earned in the third quarter of Ms. Tanner’s account?

2. What is the balance in her account after three quarters?

3. How much interest is earned in the fourth quarter?

4. What is the balance in her account after one year?

5. Suppose Ms. Tanner’s account is compounded semiannually. What is the balance at the end of six months?

6. What is the balance after one year if her account is compounded semiannually?


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-9

Study Guide and InterventionWeighted Averages

2-9

PDF Pass


Mixture Problems Mixture Problems are problems where two or more parts are combined into a whole. They involve weighted averages. In a mixture problem, the weight is usually a price or a percent of something.

Weighted AverageThe weighted average M of a set of data is the sum of the product of each number in the set

and its weight divided by the sum of all the weights.

COOKIES Delectable Cookie Company sells chocolate chip cookies for $6.95 per pound and white chocolate cookies for $5.95 per pound. How many pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies to obtain a mixture that sells for $6.75 per pound.

Let w = the number of pounds of chocolate chip cookies

Number of Pounds Price per Pound Total Price

Chocolate Chip w 6.95 6.95wWhite Chocolate 4 5.95 4(5.95)

Mixture w + 4 6.75 6.75(w + 4)

Equation: 6.95w + 4(5.95) = 6.75(w + 4)Solve the equation.

6.95w + 4(5.95) = 6.75(w + 4) Original equation

6.95w + 23.80 = 6.75w + 27 Simplify.

6.95w + 23.80 - 6.75w = 6.75w + 27 - 6.75w Subtract 6.75w from each side.

0.2w + 23.80 = 27 Simplify.

0.2w + 23.80 - 23.80 = 27 - 23.80 Subtract 23.80 from each side.

0.2w = 3.2 Simplify.

w = 16 Simplify.

16 pounds of chocolate chip cookies should be mixed with 4 pounds of white chocolate cookies.

Exercises 1. SOLUTIONS How many grams of sugar must be added to 60 grams of a solution that is

32% sugar to obtain a solution that is 50% sugar?

2. NUTS The Quik Mart has two kinds of nuts. Pecans sell for $1.55 per pound and walnuts sell for $1.95 per pound. How many pounds of walnuts must be added to 15 pounds of pecans to make a mixture that sells for $1.75 per pound?

3. INVESTMENTS Alice Gleason invested a portion of $32,000 at 9% interest and the balance at 11% interest. How much did she invest at each rate if her total income from both investments was $3200.

4. MILK Whole milk is 4% butterfat. How much skim milk with 0% butterfat should be added to 32 ounces of whole milk to obtain a mixture that is 2.5% butterfat?

Example


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

2-9 Study Guide and Intervention (continued)

Weighted Averages

PDF Pass


Uniform Motion Problems Motion problems are another application of weighted averages. Uniform motion problems are problems where an object moves at a certain speed, or rate. Use the formula d = rt to solve these problems, where d is the distance, r is the rate, and t is the time.

DRIVING Bill Gutierrez drove at a speed of 65 miles per hour on an expressway for 2 hours. He then drove for 1.5 hours at a speed of 45 miles per hour on a state highway. What was his average speed?

M = 65 . 2 + 45 . 1.5 −

2 + 1.5 Defi nition of weighted average

≈ 56.4 Simplify.

Bill drove at an average speed of about 56.4 miles per hour.

Exercises 1. TRAVEL Mr. Anders and Ms. Rich each drove home from a business meeting.

Mr. Anders traveled east at 100 kilometers per hour and Ms. Rich traveled west at 80 kilometers per hours. In how many hours were they 100 kilometers apart.

2. AIRPLANES An airplane flies 750 miles due west in 1 1 −

2 hours and 750 miles due south

in 2 hours. What is the average speed of the airplane?

3. TRACK Sprinter A runs 100 meters in 15 seconds, while sprinter B starts 1.5 seconds later and runs 100 meters in 14 seconds. If each of them runs at a constant rate, who is further in 10 seconds after the start of the race? Explain.

4. TRAINS An express train travels 90 kilometers per hour from Smallville to Megatown. A local train takes 2.5 hours longer to travel the same distance at 50 kilometers per hour. How far apart are Smallville and Megatown?

5. CYCLING Two cyclists begin traveling in the same direction on the same bike path. One travels at 15 miles per hour, and the other travels at 12 miles per hour. When will the cyclists be 10 miles apart?

6. TRAINS Two trains leave Chicago, one traveling east at 30 miles per hour and one traveling west at 40 miles per hour. When will the trains be 210 miles apart?

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-9

Skills PracticeWeighted Averages

2-9

PDF Pass


1. SEASONING A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheila wants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let b represent the amount of basil Sheila should add to the 20% blend.

a. Complete the table representing the problem.

Ounces Amount of Basil

20% Basil Blend

100% Basil

30% Basil Blend

b. Write an equation to represent the problem.

c. How many ounces of basil should Sheila use to make the 30% blend?

d. How many ounces of the 20% blend should she use?

2. HIKING At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The first group, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, and cooking equipment. The second group, hiking at an average rate of 2 miles per hour, carries food and water. Let t represent the hiking time.

a. Copy and complete the table representing the problem.

r t d = rt

First group of hikers

Second group of hikers

b. Write an equation using t that describes the distances traveled.

c. How long will it be until the two groups of hikers meet?

3. SALES Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts that cost $3.00 per pound. He mixes 10 pounds at a time.

a. How many pounds of Virginia peanuts does Sergio use?

b. How many pounds of Spanish peanuts does Sergio use?


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PracticeWeighted Averages

2-9

PDF Pass


1. GRASS SEED A nursery sells Kentucky Blue Grass seed for $5.75 per pound and Tall Fescue seed for $4.50 per pound. The nursery sells a mixture of the two kinds of seed for $5.25 per pound. Let k represent the amount of Kentucky Blue Grass seed the nursery uses in 5 pounds of the mixture.

a. Complete the table representing the problem.

Number of Pounds Price per Pound Cost

Kentucky Blue Grass

Tall Fescue

Mixture

b. Write an equation to represent the problem.

c. How much Kentucky Blue Grass does the nursery use in 5 pounds of the mixture?

d. How much Tall Fescue does the nursery use in 5 pounds of the mixture?

2. TRAVEL Two commuter trains carry passengers between two cities, one traveling east, and the other west, on different tracks. Their respective stations are 150 miles apart. Both trains leave at the same time, one traveling at an average speed of 55 miles per hour and the other at an average speed of 65 miles per hour. Let t represent the time until the trains pass each other.

a. Copy and complete the table representing the problem.

r t d = rt

First Train

Second Train

b. Write an equation using t that describes the distances traveled.

c. How long after departing will the trains pass each other?

3. TRAVEL Two trains leave Raleigh at the same time, one traveling north, and the other south. The first train travels at 50 miles per hour and the second at 60 miles per hour. In how many hours will the trains be 275 miles apart?

4. JUICE A pineapple drink contains 15% pineapple juice. How much pure pineapple juice should be added to 8 quarts of the pineapple drink to obtain a mixture containing 50% pineapple juice?


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Less

on

2-9

Word Problem PracticeWeighted Averages

2-9

PDF Pass


1. DRIVING The drive from New York City to Boston is about 240 miles. It took Samir 5 hours to drive one way, but due to severe weather it took him 6.5 hours for the return trip. What was his average speed round trip? Round the answer to the nearest hundredth.

2. GRADES In math classes at Gorbine High School, all tests are given double the weight of a quiz or homework score when calculating grades. Use Donna’s grade record sheet to determine her average grade so far this term.

3. MIXTURE Keith wants to create a drink that is 40% juice. How much of a 10% juice solution should he add to 100 milliliters of 100% grape juice to obtain the 40% mixture?

4. BUSINESS Mrs. Winship sells chocolate fudge for $7.50 per pound and peanut butter fudge for $7.00 per pound. The total number of pounds sold on Saturday was 146 and the total amount of money collected was $1065. How many pounds of each type of fudge were sold?

5. TRAINS Two trains are 5000 feet apart, heading toward each other, but on separate parallel straight tracks, Train A is traveling at 45 miles per hour and Train B is traveling at 24 miles per hour.

a. Change 45 miles per hour and 24 miles per hour into feet per second.

b. About how far will each train travel before they meet? Round your answers to the nearest hundredth.

c. In how many seconds will Train A and Train B meet?

Assignment Grade

Homework chapter 1 95

Quiz chapter 1 80

Test chapter 1 92

Homework chapter 2 93

Quiz chapter 2 96

Test chapter 2 81


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Enrichment2-9

PDF Pass


Expected ValueExpected value is the average return of an event over repeated trial. Expected value is also a form of weighted average and can be used to determine whether or not you should play a game based on what the expected value of your winnings is. It can also be used to determine the expected length of a game.

You are rolling a die to determine the number of candy bars you will win at a school fair. If you roll a one, you get 12 candy bars. If you roll a two or a three, you get 3 candy bars. If you roll a four, five or six, you get 2 candy bars.

Since there are six possibilities for what you can roll:

• 1 −

6 of the time, you will win 12 candy bars.

• 2 −

6 or 1 −


• 3 −

6 or 1 −


The expected value is 1 −

6 (12) + 1 −

3 (3) + 1 −

2 (2) or 4 candy bars.

Therefore, if you played the game 100 times, you could expect to win about 4 candy bars each time.

ExercisesFind the expected value of each of the following events.

1. You are flipping a coin. If you flip heads, you win $5.00. If you flip tails, you win $1.00.

2. You are rolling a die to determine the number of candy bars you will win at a school fair. If you roll a 1, you get 18 candy bars. If you roll a 2 or a 3, you get 6 candy bars. If you roll a 4, 5 or 6, you get 0 candy bars.

3. You are rolling a die to determine the amount of money you will win at a school fair. If you roll a 1, you get $12.00. If you roll a 2 or a 3, you get $3.00. If you roll a 4, 5 or 6, you owe $2.00.

4. You are flipping a coin. If you flip heads, you win $10. If you flip tails, you win $2.

5. You are rolling a die to determine the number of candy bars you will win at a school fair. If you roll a 1, you get 24 candy bars. If you roll a 2 or a 3, you get 6 candy bars. If you roll a 4, 5 or 6, you get none.

Example


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Ass

essm

ent

Student Recording SheetUse this recording sheet with pages 148–149 of the Student Edition.

PDF Pass


2

Read each question. Then fill in the correct answer.

1. A B C D

2. F G H J

3. A B C D

4. F G H J

5. A B C D

6. F G H J

7. A B C D

8. F G H J

Multiple Choice

Record your answer in the blank.

For gridded response questions, also enter your answer in the grid by writing each number or symbol in a box. Then fill in the corresponding circle for that number or symbol.

Short Response/Gridded Response

Extended Response

Record your answers for Question 15 on the back of this paper.

9.

10. (grid in)

11. (grid in)

12.

13. (grid in)

14.

10. 11.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

13.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

. . . . .

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

061_072_ALG1_A_CRM_C02_AS_661315.indd 61061_072_ALG1_A_CRM_C02_AS_661315.indd 61 12/22/10 12:21 PM12/22/10 12:21 PM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Rubric for Scoring Extended Response

PDF Pass


2

General Scoring Guidelines

• If a student gives only a correct numerical answer to a problem but does not show how he or she arrived at the answer, the student will be awarded only 1 credit. All extended-response questions require the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of the question. For example, if a question has three parts, the correct response to one or two parts of the question that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing that the answer checks or is correct is not considered a complete response for full credit.

Exercise 15 Rubric

Score Specifi c Criteria

4 A correct solution that is supported by well-developed, accurate explanations. In part a, students show an understanding that x visits for a yearly member cost 120 + 2x and x visits for a nonmember cost x(12 + 5 + 5) or 22x. The total cost for members and nonmembers will be the same when 120 + 2x = 22x. The equation is solved correctly as x = 6. In part b, students substitute 6 in either expression and solve to find the total cost to be $132. In part c, students explain that Georgena is better off buying a membership only if she plans to visit more than 6 times.

3 A generally correct solution, but may contain minor flaws in reasoning or computation.

2 A partially correct interpretation and/or solution to the problem.1 A correct solution with no evidence or explanation.0 An incorrect solution indicating no mathematical understanding of the concept or

task, or no solution is given.


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

Ass

essm

ent

NAME DATE PERIOD

NAME DATE PERIOD NAME DATE PERIOD

Chapter 2 Quiz 2 (Lessons 2-4 and 2-5)

Chapter 2 Quiz 1(Lessons 2-1 through 2-3)

PDF Pass


2

2

SCORE


1. The difference of the square of y and twelve is the same asthe product of five and x.


2. 2b - 10 = 4 3. y + 3x2 = 5x

Solve each equation.

4. d - 8 = 6 5. -28 = p + 21

6. -7x = 63 7. -

t −

5 = -8

8. 3x + 8 = 29 9. a −

6 - 5 = 9

10. MULTIPLE CHOICE Solve 5r −

2 - 6 = 19.

A 2.5 B 5 C -5.25 D 10


1. 7n + 6 = 4n - 9 2. 3b - 13 + 4b = 7b + 1

3. 5 - 3(w + 4) = w - 7 4. 2x - 5(x - 3) = 2(x - 10)

5. MULTIPLE CHOICE Solve -6(2r + 8) = -10(r - 3).

A -11 B -156 C -39 D 9

Evaluate each expression if h = 6 and w = -3.

6. 5 + ⎪2w⎥ 7. ⎪4 - h⎥ - w

8. ⎪2 - w - h⎥ - h


9. ⎪7 - 2q

⎥ = 3 10. ⎪4x - 2⎥ = 26

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

SCORE


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

NAME DATE PERIOD

Chapter 2 Quiz 4 (Lessons 2-8 and 2-9)

Chapter 2 Quiz 3(Lessons 2-6 and 2-7)

PDF Pass


2 SCORE


1. 5 −

7 , 20 −

28 2. 11 −

13 , 22 −

25 3. 4.2 −

6.3 , 0.3 −

0.5

Solve each proportion.

4. 3 −

4 = n −

20 5. 6 −

4 = x −

18 6. 33 −

b = 15 −

45

For Questions 7 and 8, state whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change.


9. The cost of a compact disc is $18. If the sales tax is 6%, find the total price.

10. MULTIPLE CHOICE A store sells a certain digital camera model for $108. During a special promotion, the camera is discounted by 30 percent. What is the discounted price?

A $32.40 B $75.60 C $78.00 D $140.40

For Questions 1 and 2, solve each equation or formula for the variable specified.

1. nx - r = p, for x 2. x - b − a = c, for b

3. A chemist needs a 30% iron alloy. How many grams of a 70% iron alloy must be mixed with 16 grams of a 20% iron alloy to obtain the required 30% alloy?

4. MULTIPLE CHOICE On Mary’s walk she covered the 3-mile distance to the park in one hour. However, the return trip took her one and a half hours. What was her average speed for the round trip?

A 2.4 mph B 2.5 mph C 2.8 mph D 3.9 mph

5. The formula p = 2� + 2w represents the perimeter of a rectangle. In this formula, � is the length of the rectangle and w is the width. Solve the formula for �. Find the length when the width is 4 meters and the perimeter is 36 meters.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

2 SCORE


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Mid-Chapter Test (Lessons 2-1 through 2-5)

PDF Pass


2 SCORE

Write the letter for the correct answer in the blank at the right of each question.

1. Translate the following sentence into an equation.The product of five and the sum of a number x and three is twelve.

A 5 + 3x = 12 C 5x + 3 =12 B 5(x + 3) =12 D 5x + 3 = x

2. Solve y + (-16) = -12. F 192 G -28 H 3 −

4 J 4

3. Solve -

a −

6

+ 5 = 2. A 18 B -6 C 1 −

2 D -9

4. Solve 3 −

5 y = -9.

F - 5 2 −

5 G -5 H -15 J -

5 −

9

5. Solve -6d = -42. A -48 B 7 C -36 D 252

6. Evaluate 15 - ⎪2 - 3k⎥ if k = 2. F 7 G 11 H 14 J 19

Part II

7. Translate 4n = x (5 - n) into a sentence.

For Questions 8–10, solve each equation.

8. 5(12 - 3p) = 15p + 60

9. 3(y - 2) = 6(y - 1) - 3y

10. 3a + 21 = 7 - 4a

11. Liza earned some money delivering newspapers. She boughta battery for $1.95, and gave her mother $30. She bought a ring for $7.20, and then spent half of the remaining money on a radio. If Liza has $38.50 left, how much money did she earn delivering newspapers?

12. Solve ⎪2x - 3⎥ = 7. Then graph the solution set.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Part I

-3 -2 -1 0 1 2 3 4 5


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Vocabulary Test

PDF Pass


2 SCORE

Choose a term from the list above that best matches each phrase.

1. a comparison of two numbers by division 1.

2. the sum of the product of the number of units and the value 2. per unit divided by the number of units

3. percent of increase or decrease 3.

4. a ratio of two measurements having different units of measure 4.

5. an equation with more than one operation 5.

6. the number of one item being compared to 1 of another item 6.

7. equations that are true for all values of variables 7.

Define each term in your own words.

8. proportion

9. formula

dimensional analysisequivalent equationformulaidentitymulti-step equation

percent of changeproportionrateratio

scale modelsolve an equationunit rateweighted average


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 1

PDF Pass


2 SCORE


1. Translate the following sentence into an equation.Twice a number m minus three equals the sum of m and five.

A 2(m - 3) = m + 5 C 2m - 3 = 5m

B 2m - 3 = m + 5 D 2(m - 3) = 5m

2. Translate the following equation into a verbal sentence. x + 5 = 2(7 + x)

F The quotient of x and five is two times seven plus x. G The number x plus five is two times the sum of seven and x. H The number x plus five is two times seven plus x. J The product of x and five is the sum of two times seven and x.

3. Solve y - 18 = -3. A -21 B 21 C -15 D 15

4. Solve 5n = 35. F 30 G 7 H 40 J 165

5. Solve 3 −

5 x = 15.

A 9 B 5 C 25 D 75

6. Solve 2t + 1 = 3. F 1 G -1 H 2 J -2

7. A number is added to 9. The result is then multiplied by 4 to give a new result of 120. What is the number?A 21 B 39 C 489 D 4(n + 9) + 120

8. Evaluate ⎪2b - 5⎥ + 1 if b = 1. F -2 G 2 H 4 J -8

9. Solve ⎪c - 5⎥ = 7. A Ø B {-4, 4} C {-4, 6} D {-2, 12}

10. Which ratio forms a proportion with 7 −

14 ?

F 4 −

9 G 5 −

12 H 2 −

5 J 3 −

6

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 1 (continued)

PDF Pass


2

11. Solve the proportion 2 −

7 = x −

42 .

A 1 −

2 B 12 C 2 −

7 D 6

12. Solve 3t - 6 = t -2.F -2 G -4 H 2 J 1

13. Solve 4(t + 1) = 6t - 1. A 2 1 −

2 B 1 C 0 D 1 1 −

2

14. Solve 5(g - 2) + g = 6(g - 4). F all numbers G 0 H 2 J Ø

15. Solve ax - 5 = b for a. A x(b + 5) B b - 5 − x C b + 5 − x D x(b - 5)

16. Find the percent of change. original: 10 new: 12 F 12% G 25% H 20% J 18%

17. A baseball costs $4.00. If the sales tax is 5%, what is the total price?A $3.80 B $4.20 C $4.05 D $4.50

18. How many liters of pure acid must be added to 3 liters of a 50% acid solution to obtain a 75% acid solution?F 1 L G 4.5 L H 1.5 L J 3 L

19. Joe and Janna leave home at the same time, traveling in opposite directions. Joe drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will they be 510 miles apart?A 7 hours B 6 hours C 5 hours D 4 hours

20. TEMPERATURE In Death Valley, California, the highest ground temperature recorded was 94°C on July 15, 1972. In the formula

C = 5 −

9 (F - 32), C represents the temperature in degrees Celsius and F

represents the temperature in degrees Fahrenheit. To the nearest degree, what is the highest ground temperature in Death Valley in Fahrenheit?F 201°F G 84°F H 34°F J 137°F

Bonus A concrete mixture is made with 3 parts water and 5 parts cement. If 27 parts of water are being used in the current batch of concrete, how many parts of cement are being used?

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 2A

PDF Pass


2 SCORE


1. Translate the following sentence into an equation.The sum of twice a number x and 13 is two less than three times x. A 2(x + 13) + 3x - 2 C 2x + 13 = 3x - 2 B 2x + 13 = 2 - 3x D 2x + 13 = 3(x - 2)

2. Translate the following equation into a verbal sentence.3x - y = 5(y + 2x)

F Three times the difference of x and y equals five times the sum of y and two times x.

G Three times x less than y is five times y plus two times x. H The sum of three times x and y is five times y plus two times x. J Three times x minus y is five times the sum of y and two times x.

3. Solve m - 13 = 8. A 21 B -21 C 5 D -5

4. Solve 5w = -75. F 15 G -80 H -15 J 80

5. Solve -

3 −

8 y = -24.

A -9 B 9 C -64 D 64

6. Solve 5x + 3 = 23. F 4 G 5 1 −

2 H 25 J 15

7. Six is subtracted from a number. The result is divided by four. This result is added to 10 to give 30. What is the number?

A 4 B 80 C 86 D 16

8. Evaluate ⎪2d - 3n⎥ - 4 if n = 2 and d = 3. F -8 G -4 H 0 J 4

9. Solve ⎪3r - 6⎥ = 21. A {5, -5} B {9, -9} C {9, -5} D no solution

10. Which ratio forms a proportion with 25 −

35 ?

F 3 −

5 G 15 −

21 H 24 −

34 J 5 −

10

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 2A (continued)

PDF Pass


2


3c = 1 −

6 .

A 2 B 10 C 30 D 11 −

3

12. Solve 2x + 7 = 5x + 16. F -3 G 2 −

3 H -7 2 −

3 J 3

13. Solve 2 −

3 (6x + 30) = x + 5(x + 4) - 2x.

A 6 B 0 C all numbers D no solution

14. Solve -3(h - 6) = 5(2h + 3). F -

3 −

13 G 3 −

13 H -

9 −

13 J 9 −

13

15. Solve 2x - y = y for x. A 2y - 2 B y - 2 C y D 0

16. Find the percent of change. original: 80 new: 64 F 25% G 20% H 16% J 10%

17. A calculator costs $32.00. If the sales tax is 6%, what is the total price? A $31.40 B $30.08 C $32.60 D $33.92

18. How many liters of a 40% acid solution must be added to 12 liters of a 20% solution to obtain a 25% solution?

F 4 L G 1 L H 16 L J 4 −

5 L

19. Mandy begins bicycling west at 30 miles per hour at 11:00 A.M. If Liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch Mandy?

A 2:00 P.M. B 1:00 P.M. C 1:30 P.M. D 2:30 P.M.

20. GEOMETRY The formula for the volume of a cone is V = 1 −

3 πr2h where V

represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?

F 21 cm G 69.14 cm H 7 cm J 0.78 cm

Bonus A mixture of 10% acid and 90% water is added to 5 litersof pure acid. The final mixture is 40% water. How many liters of water are in the final mixture?

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 2B

PDF Pass


2 SCORE


1. Translate the following sentence into an equation. The product of five and a number y is two less than the quotient of four and y.

A 5 + y = 4 − y - 2 C 5y = 2 - 4 − y B 5y = 4 − y - 2 D 5 + y = 2 - 4 − y

2. Translate the following equation into a verbal sentence. x(7 - 5y) = x −

2

F x times seven minus five times y equals x divided by two. G The product of x and seven minus five times y equals the quotient of

x and two. H x times the difference of seven and the product of five and y equals

the quotient of x and two. J x times the sum of seven and five times y equals x divided by two.

3. Solve x - 12 = 5.

A -17 B -7 C 17 D 7

4. Solve 6z = -84.

F -90 G -78 H -14 J -504

5. Solve - 4 −

7 k = -28.

A 49 B -49 C 16 D -16

6. Solve 2 + 7y = 44.

F 6 4 − y G 35 H 49 J 6

7. A number is divided by four. The result is added to five. This result is multiplied by three to give 27. What is the number?

A 16 B 1 C 21 1 −

2 D 3 1 −

2

8. Evaluate ⎪3f - 2g⎥ + 2 if f = -2 and g = 1. F -2 G 4 H 6 J 10

9. Solve ⎪2n + 5⎥ = 11. A {3, -3} B {3, -8} C {8, -8} D no solution

10. What ratio forms a proportion with 8 −

36 ?

F 1 −

4 G 6 −

27 H 7 −

30 J 2 −

7

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 2B (continued)

PDF Pass


2


8 = 7 −

2h .

A 4 B 28 C 56 D 16

12. Solve 9a + 28 = 4a + 3. F -30 G -20 H 6 1 −

5 J -5

13. Solve 3x + 4(x - 8) - x =

3 −

5 (10x + 15).

A 0 B all numbers C no solution D 41

14. Solve 4(3r - 2) = -3(r + 7).

F -

13 −

15 G -1 4 −

15 H 1 14 −

15 J -13

15. Solve 3b = 6v - 3b, for v. A 6b - 6 B b C b - 6 D 0

16. Find the percent of change. original: 45 new: 54

F 33 1 −

3 % G 25% H 16 2 −

3 % J 20%

17. Find the discounted price. radio: $45.00 discount: 30% A $15.00 B $31.50 C $36.00 D $42.00

18. Nature Drinks wants to combine orange juice they sell for $0.09 per ounce with guava juice they sell for $0.14 per ounce to create an orange-guava drink. How many ounces of orange juice should they use to create a 16-ounce drink that would sell for $1.74?

F 10 oz G 6 oz H 16 oz J 0 oz

19. Teri begins walking east at 2 miles per hour at 1:00 P.M. If Cindy leaves from the same point 30 minutes later walking east at 3 miles per hour, when will she catch Teri?

A 2:30 P.M. B 1:30 P.M. C 2:00 P.M. D 3:00 P.M.

20. GEOMETRY The formula for the volume of a cone is V =

1 −

3 πr2h, where V

represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 110 cubic centimeters and a base with a radius of 5 centimeters?

F 21 cm G 0.47 cm H 4.2 cm J 41.49 cm

Bonus In a bag of blue, green, and red marbles, 50% are blueand 30% are green. There are 6 red marbles in the bag. If you increase the number of blue marbles by 40%, how many blue marbles will be in the bag?

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 2C

PDF Pass


2 SCORE

1. Translate the following sentence into an equation. A number x subtracted from 36 is three times the sum of four and x.

2. Translate the following equation into a verbal sentence.3(x + y) = 2y - x


3. 12 + r = 3

4. -12 = p - 7

5. -7b = -35

6. -

5 −

8 w = -9

7. 9 −

25 =

p −

125

8. -3a + 4 = -14

For Questions 9 and 10, write an equation for each problem. Then solve the equation.

9. What number decreased by 3.5 equals 12.7?

10. Twelve is added to the product of a number and 5. The result is -3. Find the number.

11. Julie cashed a paycheck and repaid her brother $10 thatshe had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.45 and had $17.75 left. How much did Julie receive when she cashed her paycheck?

12. Evaluate ⎪4t + n⎥ if t = -2 and n = 5.

For Questions 13 and 14, solve each equation. Then graph the solution set.

13. ⎪5t - 1⎥ = 6

14. ⎪2a + 1⎥ = 1

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14. -4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 2C (continued)

PDF Pass


2

15. Use cross products to determine whether the pair of

ratios 4 −

6 and 14 −

21 form a proportion. Write yes or no.


15 =

18 −

b .


17. -x + 4 = x + 6

18. 5n + 7 = 7(n + 1) - 2n

19. -4(p + 2) + 8 = 2(p - 1) - 7p + 15

20. Solve a −

b x - c = 0 for x.

21. State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. original: 55 new: 44

22. A shirt costs $12.00. If the sales tax is 7%, find the total cost.

23. How many liters of a 90% acid solution must be added to 6 liters of a 15% acid solution to obtain a 40% acid solution?

24. A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?

25. GEOMETRY A container company wants to make a cylindrical can with a volume of 1188 cubic inches. The formula V = πr2h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder’s base, and h represents the height of the cylinder. Solve for h. What height should the company make the can if the radius of the base must be 6 inches?

Bonus A clown is preparing for a party by inflating one balloon for every invited guest. Just when she has half of the necessary balloons inflated, 3 of them pop. She inflates 5 more balloons, and two pop. Then 6 balloons are carried away by the wind. She finishes by inflating 16 more balloons, and then learns that only 12 guests will attend the party. How many extra balloons did the clown inflate?

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 2D

PDF Pass


2 SCORE

1. Translate the following sentence into an equation. A number n added to 18 is seven times the difference of n and three.

2. Translate the following equation into a verbal sentence.

3 − y - 5 = x(y + 7)


3. 7 + t = 11

4. -5 = v - 12

5. -8x = -56

6. -

7 −

9 y = -6

7. 10 −

27 = a −

135

8. 3 - 5b = -32


9. What number decreased by 8.1 equals 4.9?

10. Fifteen is added to the product of a number and 6. The result is 9. Find the number.

11. During an evening out, Dean paid a cab driver $20. He then spent $25 on dinner and half of his remaining money on a painting. He bought an umbrella for $23.75 and had $42.15 left. How much money did Dean have at the beginning of the weekend?

12. Evaluate ⎪3t - n⎥ if t = -3 and n = 2.

For Questions 13 and 14, solve each equation. Then graph the solution set.

13. ⎪2t + 4⎥ = 2

14. ⎪r + 3⎥ = 1

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 2D (continued)

PDF Pass


2

15. Use cross products to determine whether the pair of ratios 14 −

17 and 39 −



12 =

15 − a .


17. 9 - t = t + 3

18. 2(y - 6) = 3y + 12 - y

19. 17 + 3(z - 2) - 11z = -7(z + 2) + 14

20. Solve r − n + t = 4v for r.

21. State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. original: 60, new: 75

22. Find the discounted price. flashlight: $18.00 discount: 25%

23. Nature’s Best wants to combine nuts they sell for $3.60 a pound with dried fruit they sell for $2.40 a pound to create a trail mix. How much of each snack should they use to make 10 pounds of trail mix that would sell for $3.30 a pound?

24. Paula leaves home driving 40 miles per hour. One hour later, her brother Dan leaves home, driving in the same direction at a speed of 50 miles per hour. How long will it take Dan to catch up to Paula?

25. GEOMETRY A container company wants to make a cylindrical cardboard container with a volume of 4752 cubic inches. The formula V = πr2h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder’s base, and h represents the height of the cylinder. Solve for h. What height should the company make the container if the radius of the base must be 9 inches?

Bonus A store has all board games on sale for 25% off the regular price. A checker set has a sale price of $12. It is then moved to a clearance table where every item is discounted 40% off its regular price. What is the clearance price of the checker set?

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Test, Form 3

PDF Pass


2 SCORE

1. Translate the following into an equation. A number x is decreased by 45. The result is then divided by 12. Then 20 is added to this new result to give a final result of five times the difference of 32 and the number x.

2. Translate the following equation into a verbal sentence.5(2x + 3y) = y2

- 2x3


3. n + 39 = 12

4. w + (-8) = -21

5. -6n = 16

6. 3 −

4 h = -

45 −

52

7. -

a −

6 + 7 = -14

8. If x - 5 = 12, what is the value of x - 9?


9. Three-fifths of what number equals one?

10. The product of 2 more than a number and 10 is 36 more than 8 times the number. What is the number?

11. Evaluate 2|m - 3x| - p if m = -1, x = 2, and p = 4.

12. Solve 2 ⎪

x −

2 + 3

⎥

= 1. Then graph the solution set.

13. Shyam invested money in the stock market. In the first year, his stock increased 20%. He paid his stock broker $300 and then lost $450. He withdrew $500, and then his remaining investment doubled. Shyam’s investment is now worth $7100. How much was Shyam’s original investment?

14. Use cross products to determine whether the pair of ratios 42 −

48 and 63 −


15. A blueprint for a house states that 2 inches represents 8 feet. If the width of a window is 2.5 inches on the blueprint, what is the width of the actual window?

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

-8 -7 -6 -4 -3 -2 -1-5 0


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Chapter 2 Test, Form 3 (continued)

PDF Pass


2

16. Solve the proportion t + 4 −

t - 2 = 1 −

4 .

For Questions 17 and 18, solve each equation.

17. 6 - 2y = 7y + 13

18. 5(7 - a) - 3(a + 4) - 4 = 4(a -3) + 7

19. Solve ax - n = r for x.

20. Solve 4x + t − r = y for x.

21. State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change.

original: 75, new: 84

22. A jacket costs $75.00 retail. A warehouse outlet discounts the price by 20%. If the sales tax is 6%, find the final price.

23. Calvin invested $7500 for one year, part at 12% annual interest and the rest at 10% annual interest. His total interest for the year was $890. How much money did he invest at 12%?

24. Two airplanes leave the Atlanta airport at the same time, traveling in opposite directions. One plane travels 30 miles per hour faster than the other. After 3 hours, the planes are 3150 miles apart. What is the rate of each plane?

25. PHYSICS A ball is thrown straight up at an initial velocity of 53 feet per second. In the first 1.5 seconds, it travels

42 feet. The formula x = (

u + t − n ) t represents the vertical

distance x that an object travels in t seconds, where u represents the initial velocity of the object and n represents the velocity of the object at the end of t seconds. Find the velocity of the ball at the end of 1.5 seconds.

Bonus Paloma Rey drove to work on Wednesday at 40 miles per hour and arrived one minute late. She left home at the same time on Thursday, drove 45 miles per hour, and arrived one minute early. How far does Ms. Rey drive to work?

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Chapter 2 Extended-Response Test

PDF Pass


2 SCORE

Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problem.

1. Phrase 1: x times y plus z; Phrase 2: x times the sum of y and z

a. Discuss what is different between the two phrases.

b. Find values for x, y and z that make the two phrases equal.

2. a. Solve ry + z

− m - t = x for y, and explain each step in your solution.

b. Would there be any limitations for the value of each variable? If so, explain the limitation.

3. You buy a stereo at a local store. The stereo has been discounted by 10%. The store then charges 10% tax.

a. Compare the final price with the original price.

b. Would the final price be different if the tax was added first and then the discount was applied to this new amount?

4. Tony and Ivia started walking south from the same location at the same time. Ivia walked 8 miles and walked 1 mile per hour faster than Tony who walked 6 miles. They each walked for the same amount of time.

a. Describe how a proportion could be used to find the rate that each person walked.

b. The next day they both walked 6 miles, and Ivia again walked 1 mile per hour faster than Tony, who walked 3 miles per hour. Determine whether a proportion could be used to find how long each person walked.

5. a. Write four equivalent equations to x = 8 using one of the four operations of addition, subtraction, multiplication and division for each equivalent equation. Use each operation only once.

b. Write an equivalent equation to x = 8 that has the variable x on both sides.

c. Determine if n −

6 = 15 −

18 and 2(n + 1) = 3(n - 1) are equivalent equations. Determine if

either equation is equivalent to any of the equations created for parts a and b.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

PDF Pass


2 SCORE Standardized Test Practice(Chapters 1–2)

1. Write an algebraic expression for the following verbal expressionthe sum of n and 5. (Lesson 1-1)

A 5n B n −

5 C n + 5 D n - 5

2. Determine which of the following relations is a function. (Lesson 1-7)

F {(-4, 3), (−2, −2), (0, 2), (0, 5)} G {(−3, 1), (−3, 3), (−2, −1), (0, 5)}H {(−4, −1), (−2, −1), (−1, −1), (3, 3)}J {(2, −5), {−1, −1), (0, 4), (2, −3)}

3. Simplify the expression 7(x - y) - 2(y - x) + 4x. (Lesson 1-4)

A 13x - 9y B 9x - 5y C 9x - 9y D 13x - 5y

4. Evaluate a(b - c2) if a = 2 −

3 , b = 3 −

4 , and c = 1 −

2 . (Lesson 1-2)

F 1 −

6 G 1 −

3 H 1 −

4 J 2 −

3

5. Solve the proportion a −

25 = 9 −

45 . (Lesson 2-6)

A 7.8 B 16.2 C 125 D 5

6. Jackson’s meal cost $15.40. How much money should he leave for a 15% tip? (Lesson 2-7)

F $0.23 G $2.31 H $23.10 J $231.00

7. Solve -

3 −

4 y = 8 −

20 . (Lesson 2-2)

A 2 −

5 B -

3 −

10 C 8 −

15 D -

8 −

15

8. Which equation has a solution of -2? (Lesson 2-3)

F 4n + 3 = 11 H 5(1 + n) = -5G 4 = 3n - 2 J 3(n + 1) = 2

9. A car dealership has 180 cars on their lot. If they increase their inventory by 25%, how many cars will be on the lot? (Lesson 2-7)

A 230 B 225 C 135 D 205

Part 1: Multiple Choice

Instructions: Fill in the appropriate circle for the best answer.

1.

2.

3.

4.

5.

6.

7.

8.

9. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

A B C D

F G H J


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Standardized Test Practice (continued)

PDF Pass


2

10. Translate the following sentence into an equation. The quotient of 24 and x equals 14 minus 2 times x. (Lesson 2-1)

F 24x = 14 - 2x H 24 − x = 14 - 2x

G 24x = 2x - 14 J 24 − x = 2x - 14

11. Evaluate 26. (Lesson 1-2)

A 12 B 32 C 64 D 128

12. Which pair of ratios forms a proportion? (Lesson 2-6)

F 2 −

3 and 4 −

9 G 5 −

15 and 4 −

12 H 4 −

12 and 6 −

24 J 1 −

9 and 9 −

10

13. Evaluate 14 -

(

1 −

4

)

(17 - 5). (Lesson 1-2)

A 17 B 34 C 11 D 120

14. Evaluate 21 ÷ 3 + 4 � 2. (Lesson 1-2)

F 15 G 22 H 1.9 J 9

10.

11.

12.

13.

14. F G H J

A B C D

F G H J

A B C D

F G H J

15. Solve 2 + 5x = 10 - 3x. (Lesson 2-4) 16. Sasha drove from her house to the grocery store in 20 minutes. Her return trip took 15 minutes. If the store is 7 miles from her house, what was Sasha’s average speed for the round trip, in miles per hour? (Lesson 2-9)

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

Part 2: Gridded Response

Instructions: Enter your answer by writing each digit of the answer in a column box

and then shading in the appropriate circle that corresponds to that entry.


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Standardized Test Practice (continued)

PDF Pass


2

17. Evaluate 3y - x2z if x = 2, y = 14, and z = 5. (Lesson 1-2)

18. Simplify 2(u + 3x) + 3(u + x). (Lesson 1-3)

19. Miguel was riding his bike to school. He got halfway there and realized he had forgotten his backpack. He turned around, went home, retrieved his backpack, and continued his ride to school. Sketch a reasonable graph to show his distance from school from the time he started to the time he arrived at school. Assume his rate is always the same. (Lesson 1-6)

20. Translate the following sentence into an algebraic equation. Nine times a number y subtracted from 85 is seven times the sum of four and y. (Lesson 2-1)

21. Solve the following problem by working backward. Three is added to a number. The result is divided by two, and then the new result is added to eighteen. The final result is 35. What is the number? (Lesson 2-3)

For Questions 22–24, solve each equation. (Lessons 2-2 through 2-4)

22. -27 = -6 - 3p 23. 7a + 2 = 3a - 10

24. 2(x - 3) + 6x = 3(9 - x)

25. Solve t = m − x + p for m. (Lesson 2-8)

26. How many liters of water must be added to 7 liters of a 20% acid solution to obtain a 10% acid solution? (Lesson 2-9)

27. Stacy bought a skateboard at a local sporting goods store. The skateboard was on sale for 10% off the original price. The store then charges 10% sales tax. (Lesson 2-7)

a. How does the original price compare to the final price?

b. Would the final price be different if the 10% sales tax was added first and then the 10% discount was applied to this new amount?

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27a.

27b.

y

xO

Part 3: Short Response

Instructions: Write your answers in the space provided.


Ass

essm

ent

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

NAME DATE PERIOD

Unit 1 Test(Chapters 1–2)

PDF Pass


2 SCORE

1. Write a verbal expression for 4r + 9.

2. Write an algebraic expression for the difference of 5 and n cubed.

3. Evaluate 2x + 5y2 - 3z if x = 6, y = 4, and z = 7.

4. Name the property used in the equation 1 = 6n. Then find the value of n.

For Questions 5–7, simplify each expression.

5. 2t2 + 5t2

+ 3t

6. 7(r + 2t) - 5t

7. 5(4a + b) + 3a + b

8. Find the solution set for 3b - 4 = 8 if the replacement setis {1, 2, 3, 4, 5}.

For Questions 9–10, determine whether each relation is a function.

9. {(1, 5), (2, 4), (3, 5), (4, 9)} 10. x = -2

11. If f (n) = 6 - 2n, find f (-1).

12. True or False: A linear graph can have a maximum or a minimum.

13. Draw a reasonable graph showing the relationship between the temperature of a pizza as it is removed from an oven and placed on a counter at room temperature, and time.

14. The sides of an equilateral triangle measure (2x + 4) units. What is the perimeter?

15. Translate m2 - 4 = 2r + 1 into a sentence.

16. Write a problem based on the given information.

h = the height of a math textbook; h + 2 = the height of a science textbook 4h + 2 (h + 2)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

Time

Tem

per

atu

re (

°F)


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

NAME DATE PERIOD

Unit 1 Test (continued)

PDF Pass


2


17. m - 5 = -23

18. -4 = 8 + k

19. a −

2 + 9 = 30

20. -

2 −

7 x = -16

21. 5(c + 3) = 15 + 2(2c - 1)

22. 10(a + 1) - 14a = 9 - (4a - 1)

23. 7 −

10 =

3 −

x + 1

For Questions 24 and 25, evaluate each expression if a = 3, b = 4, and c = 9.

24. 2 ⎪a - b⎥ + ⎪c⎥

25. c - b ⎪1 - a⎥

26. Solve ⎪2x - 1⎥ = 5. Then graph the solution set.

27. Determine whether 4 −

9 and 20 −

45 are equivalent ratios.

Write yes or no.

28. A magazine is on sale for 15% off the original price. If the original price of the magazine is $4.60, what is the discounted price?

29. Solve t - v − r = k, for v.

30. How many pounds of peanuts costing $3.00 a pound should be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound?

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

-2-3 -1 0 1 2 4 5 6 7 83


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass

Chapter 2 A1 Glencoe Algebra 1

Chapter Resources

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DAT

E

P

ER

IOD

Ant

icip

atio

n G

uide

Lin

ear

Eq

uati

on

s

2

Cha

pte

r 2

3 G

lenc

oe A

lgeb

ra 1

B

efor

e yo

u b

egin

Ch

ap

ter

2

•

Rea

d ea

ch s

tate

men

t.

•

Dec

ide

wh

eth

er y

ou A

gree

(A

) or

Dis

agre

e (D

) w

ith

th

e st

atem

ent.

•

Wri

te A

or

D i

n t

he

firs

t co

lum

n O

R i

f yo

u a

re n

ot s

ure

wh

eth

er y

ou a

gree

or

disa

gree

, wri

te N

S (

Not

Su

re).

A

fter

you

com

ple

te C

ha

pte

r 2

•

Rer

ead

each

sta

tem

ent

and

com

plet

e th

e la

st c

olu

mn

by

ente

rin

g an

A o

r a

D.

•

Did

an

y of

you

r op

inio

ns

abou

t th

e st

atem

ents

ch

ange

fro

m t

he

firs

t co

lum

n?

•

For

th

ose

stat

emen

ts t

hat

you

mar

k w

ith

a D

, use

a p

iece

of

pape

r to

wri

te a

n

exam

ple

of w

hy

you

dis

agre

e.

ST

EP

1A

, D, o

r N

SS

tate

men

tS

TE

P 2

A o

r D

1.

Wh

en w

riti

ng

equ

atio

ns

the

phra

ses

as m

uch

as,

is,

an

d is

id

enti

cal

to, a

ll s

ugg

est

the

equ

als

sign

. 2

. T

he

solv

ing

an e

quat

ion

str

ateg

y ca

nn

ot b

e u

sed

if a

n

eq

uat

ion

is

not

giv

en i

n t

he

prob

lem

. 3

. G

iven

a t

rue

equ

atio

n, a

ny

valu

e ca

n b

e ad

ded

or s

ubt

ract

ed

to b

oth

sid

es r

esu

ltin

g in

a t

rue

equ

atio

n.

4.

Sin

ce t

he

equ

atio

n t

- 2

3 =

54

invo

lves

su

btra

ctio

n,

subt

ract

ion

wou

ld b

e u

sed

to s

olve

for

t.

5.

To

solv

e 21

= -

7x, y

ou c

ould

div

ide

by -

7 or

mu

ltip

ly b

y -

1 −

7 .

6.

To

solv

e eq

uat

ion

s w

ith

mor

e th

an o

ne

oper

atio

n, u

ndo

op

erat

ion

s in

th

e sa

me

orde

r as

th

e O

rder

of

Ope

rati

ons.

7.

Equ

atio

ns

wit

h t

he

vari

able

on

bot

h s

ides

hav

e n

o so

luti

on.

8.

3 to

5, 3

:5, a

nd

3 −

5 a

re a

ll e

xam

ples

of

rati

os.

9.

Bec

ause

5 �

12

= 1

5 � 4

, 12

−

15

is

in p

ropo

rtio

n t

o 4 −

5 .

10.

A p

erce

nt o

f ch

ange

is f

ound

by

divi

ding

the

am

ount

of

ch

ange

by

the

orig

inal

am

ount

.

11.

Equ

atio

ns

con

tain

ing

two

vari

able

s ca

nn

ot b

e so

lved

sin

ce

vari

able

s ca

nn

ot b

e ad

ded

or s

ubt

ract

ed f

rom

eac

h s

ide

of

the

equ

atio

n.

12.

To

fin

d a

wei

ghte

d av

erag

e, e

xtre

mel

y h

igh

or

low

val

ues

ar

e n

ot i

ncl

ude

d.

Step

1

Step

2

A D A D A D D A A A D D

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

312

/22/

10

12:1

8 P

M

Lesson 2-1


NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

Wri

tin

g E

qu

ati

on

s

2-1

Cha

pte

r 2

5 G

lenc

oe A

lgeb

ra 1

Wri

te E

qu

atio

ns

Wri

tin

g eq

uat

ion

s is

on

e st

rate

gy f

or s

olvi

ng

prob

lem

s. Y

ou c

an u

se a

va

riab

le t

o re

pres

ent

an u

nsp

ecif

ied

nu

mbe

r or

mea

sure

ref

erre

d to

in

a p

robl

em. T

hen

you

ca

n w

rite

a v

erba

l ex

pres

sion

as

an a

lgeb

raic

exp

ress

ion

.

T

ran

slat

e ea

ch

sen

ten

ce i

nto

an

eq

uat

ion

or

a fo

rmu

la.

a. T

en t

imes

a n

um

ber

x i

s eq

ual

to

2.8

tim

es t

he

dif

fere

nce

y m

inu

s z.

10 ×

x =

2.8

× (

y -

z)

Th

e eq

uat

ion

is

10x

= 2

.8(y

- z

).b

. A

nu

mb

er m

min

us

8 is

th

e sa

me

as a

nu

mb

er n

div

ided

by

2.m

- 8

= n

÷ 2

Th

e eq

uat

ion

is

m -

8 =

n

−

2 .c.

Th

e ar

ea o

f a

rect

angl

e eq

ual

s th

e le

ngt

h t

imes

th

e w

idth

. Tra

nsl

ate

this

sen

ten

ce i

nto

a f

orm

ula

.L

et A

= a

rea,

ℓ =

len

gth

, an

d w

= w

idth

.F

orm

ula

: Are

a eq

ual

s le

ngt

h t

imes

w

idth

. A

= ℓ

× w

Th

e fo

rmu

la f

or t

he

area

of

a re

ctan

gle

is A

= ℓ

w.

U

se t

he

Fou

r-S

tep

P

rob

lem

-Sol

vin

g P

lan

.PO

PULA

TIO

N T

he

pop

ula

tion

of

the

Un

ited

S

tate

s in

Ju

ly 2

007

was

ab

out

301,

000,

000,

an

d t

he

lan

d a

rea

of t

he

Un

ited

Sta

tes

is

abou

t 3,

500,

000

squ

are

mil

es. F

ind

th

e av

erag

e n

um

ber

of

peo

ple

per

sq

uar

e m

ile

in t

he

Un

ited

Sta

tes.

Ste

p 1

R

ead

You

kn

ow t

hat

th

ere

are

301,

000,

000

peop

le. Y

ou w

ant

to k

now

th

e n

um

ber

of p

eopl

e pe

r sq

uar

e m

ile.

Ste

p 2

P

lan

Wri

te a

n e

quat

ion

to

repr

esen

t th

e si

tuat

ion

. Let

p r

epre

sen

t th

e n

um

ber

of

peop

le p

er s

quar

e m

ile.

3,

500,

000

× p

= 3

01,0

00,0

00S

tep

3

Sol

ve 3

,500

,000

× p

= 3

01,0

00,0

00.

3,

500,

000p

= 3

01,0

00,0

00 D

ivid

e ea

ch s

ide

by

p

= 8

6 3,

500,

000.

T

her

e ar

e 86

peo

ple

per

squ

are

mil

e.S

tep

4

Ch

eck

If t

her

e ar

e 86

peo

ple

per

squ

are

mil

e an

d th

ere

are

3,50

0,00

0 sq

uar

e m

iles

, 86

× 3

,500

,000

= 3

01,0

00,0

00.

Th

e an

swer

mak

es s

ense

.

Exer

cise

sT

ran

slat

e ea

ch s

ente

nce

in

to a

n e

qu

atio

n o

r fo

rmu

la.

1. T

hre

e ti

mes

a n

um

ber

t m

inu

s tw

elve

equ

als

fort

y.

2. O

ne-

hal

f of

th

e di

ffer

ence

of

a an

d b

is 5

4.

3. T

hre

e ti

mes

th

e su

m o

f d

an

d 4

is 3

2.

4. T

he

area

A o

f a

circ

le i

s th

e pr

odu

ct o

f π

an

d th

e ra

diu

s r

squ

ared

.

5. W

EIG

HT

LOSS

Lou

wan

ts t

o lo

se w

eigh

t to

au

diti

on f

or a

par

t in

a p

lay.

He

wei

ghs

160

pou

nds

now

. He

wan

ts t

o w

eigh

150

pou

nds

.

a.

If

p re

pres

ents

th

e n

um

ber

of p

oun

ds h

e w

ants

to

lose

, wri

te a

n e

quat

ion

to

repr

esen

t th

is s

itu

atio

n.

b

. H

ow m

any

pou

nds

doe

s h

e n

eed

to l

ose

to r

each

his

goa

l?

Exam

ple

2Ex

amp

le 1

3t -

12

= 4

0

3(d

+ 4

) =

32

A =

πr

2

160

- p

= 1

50

10 lb

1 −

2 (a

- b

) =

54

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

512

/22/

10

12:1

8 P

M

Answers (Anticipation Guide and Lesson 2-1)

A01_A14_ALG1_A_CRM_C02_AN_661315.indd A1A01_A14_ALG1_A_CRM_C02_AN_661315.indd A1 12/22/10 1:07 PM12/22/10 1:07 PM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Wri

tin

g E

qu

ati

on

s

2-1

Cha

pte

r 2

6 G

lenc

oe A

lgeb

ra 1

Wri

te V

erb

al S

ente

nce

s Yo

u c

an t

ran

slat

e eq

uat

ion

s in

to v

erba

l se

nte

nce

s.

T

ran

slat

e ea

ch e

qu

atio

n i

nto

a s

ente

nce

.

a. 4

n -

8 =

12.

4n

-

8

=

1

2F

our

tim

es n

min

us

eigh

t eq

ual

s tw

elve

.

b.

a2

+ b

2 =

c2

a

2 +

b2

=

c2

Th

e su

m o

f th

e sq

uar

es o

f a

and

b is

equ

al t

o th

e sq

uar

e of

c.

Exer

cise

sT

ran

slat

e ea

ch e

qu

atio

n i

nto

a s

ente

nce

.

1. 4

a -

5 =

23

2. 1

0 +

k =

4k

3. 6

xy =

24

4. x

2 +

y2

= 8

5. p

+ 3

= 2

p 6.

b =

1 −

3 (

h -

1)

7. 1

00 -

2x

= 8

0 8.

3(g

+ h

) =

12

9. p

2 -

2p

= 9

10

. C =

5

−

9 (

F -

32)

11. V

= 1

−

3

Bh

12

. A

= 1

−

2

hb

Exam

ple

4

tim

es a

min

us

5 is

eq

ual

to

23.

T

he

sum

of

10 a

nd

k is

eq

ual

to

4

tim

es k

.

6

tim

es t

he

pro

du

ct o

f x a

nd

y is

Th

e su

m o

f th

e sq

uar

es o

f x a

nd

eq

ual

to

24.

y is

eq

ual

to

8.

T

he

sum

of

p a

nd

3 is

eq

ual

to

b

is 1 −

3 o

f th

e d

iffer

ence

of

h a

nd

1.

2 ti

mes

p.

1

00

min

us

2 ti

mes

x is

eq

ual

3

tim

es t

he

sum

of

g a

nd

h is

12.

to

80.

T

he

squ

are

of

p m

inu

s 2

tim

es

C is

eq

ual

to

5 −

9 o

f th

e d

iffer

ence

of

p

is e

qu

al t

o 9

.

F a

nd

32.

V

is e

qu

al t

o 1 −

3 o

f th

e p

rod

uct

of

A

is e

qu

al t

o 1 −

2 o

f th

e p

rod

uct

of

B

an

d h

. h

an

d b

.

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

612

/22/

10

12:1

8 P

M

Lesson 2-1


NA

ME

DAT

E

P

ER

IOD

Skill

s Pr

acti

ceW

riti

ng

Eq

uati

on

s

2-1

Cha

pte

r 2

7 G

lenc

oe A

lgeb

ra 1

Tra

nsl

ate

each

sen

ten

ce i

nto

an

eq

uat

ion

.

1. T

wo

adde

d to

th

ree

tim

es a

nu

mbe

r m

is

the

sam

e as

18.

2. T

wic

e a

incr

ease

d by

th

e cu

be o

f a

equ

als

b.

3. S

even

les

s th

an t

he

sum

of

p an

d t

is a

s m

uch

as

6.

4. T

he

sum

of

x an

d it

s sq

uar

e is

equ

al t

o y

tim

es z

.

5. F

our

tim

es t

he

sum

of

f an

d g

is i

den

tica

l to

six

tim

es g

.

Tra

nsl

ate

each

sen

ten

ce i

nto

a f

orm

ula

.

6. T

he

peri

met

er P

of

a sq

uar

e eq

ual

s fo

ur

tim

es t

he

len

gth

of

a si

de �

.

7. T

he

area

A o

f a

squ

are

is t

he

len

gth

of

a si

de �

squ

ared

.

8. T

he

peri

met

er P

of

a tr

ian

gle

is e

qual

to

the

sum

of

the

len

gth

s of

sid

es a

, b, a

nd

c.

9. T

he

area

A o

f a

circ

le i

s pi

tim

es t

he

radi

us

r sq

uar

ed.

10. T

he

volu

me

V o

f a

rect

angu

lar

pris

m e

qual

s th

e pr

odu

ct o

f th

e le

ngt

h �

, th

e w

idth

w,

and

the

hei

ght

h.

Tra

nsl

ate

each

eq

uat

ion

in

to a

sen

ten

ce.

11. g

+ 1

0 =

3g

12. 2

p +

4t

= 2

0

13. 4

(a +

b)

= 9

a 14

. 8 -

6x

= 4

+ 2

x

15.

1 −

2 (f

+ y

) =

f -

5

16. k

2 -

n2

= 2

b

Wri

te a

pro

ble

m b

ased

on

th

e gi

ven

in

form

atio

n.

17. c

= c

ost

per

pou

nd

of p

lain

cof

fee

bean

s

18.

p =

cos

t of

din

ner

c

+ 3

= c

ost

per

pou

nd

of f

lavo

red

coff

ee b

ean

s

0.15

p =

cos

t of

a 1

5% t

ip

2c

+ (

c +

3)

= 2

1

p +

0.1

5p =

23

3m +

2 =

18

2a +

a3

= b

(p +

t)

- 7

= 6

x +

x2

= y

z

4(f

+ g

) =

6g

P =

4�

A =

�2

P =

a +

b +

c

A =

πr

2

V =

�w

h

g

plu

s 10

is t

he

sam

e as

Tw

ice

p p

lus

4 ti

mes

t is

20.

3

tim

es g

.

4

tim

es t

he

sum

of

a a

nd

b

8 m

inu

s 6

tim

es x

is 4

plu

s

is 9

tim

es a

.

2 ti

mes

x.

H

alf

of

the

sum

of

f an

d y

is

k s

qu

ared

min

us

n s

qu

ared

is

f m

inu

s 5.

twic

e b

.

S

amp

le a

nsw

er: T

he

cost

of

two

po

un

ds

S

amp

le a

nsw

er: T

he

cost

of

of

pla

in c

off

ee b

ean

s p

lus

on

e p

ou

nd

of

din

ner

plu

s a

15%

tip

was

fl

avo

red

bea

ns

is $

21. H

ow

mu

ch d

oes

$2

3. H

ow

mu

ch w

as t

he

1 p

ou

nd

of

pla

in b

ean

s co

st?

d

inn

er?

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

712

/22/

10

12:1

8 P

M

Answers (Lesson 2-1)


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Prac

tice

W

riti

ng

Eq

uati

on

s

2-1

Cha

pte

r 2

8 G

lenc

oe A

lgeb

ra 1

Tra

nsl

ate

each

sen

ten

ce i

nto

an

eq

uat

ion

.

1. F

ifty

-th

ree

plu

s fo

ur

tim

es b

is

as m

uch

as

21.

2. T

he

sum

of

five

tim

es h

an

d tw

ice

g is

equ

al t

o 23

.

3. O

ne

fou

rth

th

e su

m o

f r

and

ten

is

iden

tica

l to

r m

inu

s 4.

4. T

hre

e pl

us

the

sum

of

the

squ

ares

of

w a

nd

x is

32.

Tra

nsl

ate

each

sen

ten

ce i

nto

a f

orm

ula

.

5. D

egre

es K

elvi

n K

equ

als

273

plu

s de

gree

s C

elsi

us

C.

6. T

he

tota

l co

st C

of

gas

is t

he

pric

e p

per

gall

on t

imes

th

e n

um

ber

of g

allo

ns

g.

7. T

he

sum

S o

f th

e m

easu

res

of t

he

angl

es o

f a

poly

gon

is

equ

al t

o 18

0 ti

mes

th

e di

ffer

ence

of

th

e n

um

ber

of s

ides

n a

nd

2.

Tra

nsl

ate

each

eq

uat

ion

in

to a

sen

ten

ce.

8. r

- (

4 +

p)

= 1 −

3 r

9.

3 −

5 t

+ 2

= t

10. 9

(y2

+ x

) =

18

11.

2(m

- n

) =

x +

7

Wri

te a

pro

ble

m b

ased

on

th

e gi

ven

in

form

atio

n.

12. a

= c

ost

of o

ne

adu

lt’s

tic

ket

to z

oo

13. c

= r

egu

lar

cost

of

one

airl

ine

tick

eta

- 4

= c

ost

of o

ne

chil

dren

’s t

icke

t to

zoo

0

.20c

= a

mou

nt o

f 20%

pro

mot

iona

l dis

coun

t

2a

+ 4

(a -

4)

= 3

8

3(c

- 0

.20c

) =

330

14. G

EOG

RA

PHY

Abo

ut

15%

of

all

fede

rall

y-ow

ned

lan

d in

th

e 48

con

tigu

ous

stat

es o

f th

e U

nit

ed S

tate

s is

in

Nev

ada.

If

F r

epre

sen

ts t

he

area

of

fede

rall

y-ow

ned

lan

d in

th

ese

stat

es, a

nd

N r

epre

sen

ts t

he

port

ion

in

Nev

ada,

wri

te a

n e

quat

ion

for

th

is s

itu

atio

n.

15. F

ITN

ESS

Dea

nn

a an

d P

ietr

a ea

ch g

o fo

r w

alks

aro

un

d a

lake

a f

ew t

imes

per

wee

k. L

ast

wee

k, D

ean

na

wal

ked

7 m

iles

mor

e th

an P

ietr

a.

a.

If

p re

pres

ents

th

e n

um

ber

of m

iles

Pie

tra

wal

ked,

wri

te a

n e

quat

ion

th

at r

epre

sen

ts

the

tota

l n

um

ber

of m

iles

T t

he

two

girl

s w

alke

d.

b

. If

Pie

tra

wal

ked

9 m

iles

du

rin

g th

e w

eek,

how

man

y m

iles

did

Dea

nn

a w

alk?

c.

If

Pie

tra

wal

ked

11 m

iles

du

rin

g th

e w

eek,

how

man

y m

iles

did

th

e tw

o gi

rls

wal

k to

geth

er?

53 +

4b

= 2

1

5h +

2g

= 2

3

3 +

(w

2 +

x2 )

= 3

2

K =

273

+ C

C =

pg

S =

180

(n -

2)

r m

inu

s th

e su

m

o

f 4

and

p e

qu

als

1 −

3 t

imes

r.

Two

mo

re t

han

3 −

5 of

t eq

ual

s t.

9 ti

mes

th

e su

m

Twic

e th

e q

uan

tity

of

y s

qu

ared

an

d x

is 1

8.

m m

inu

s n

is x

plu

s 7.

S

amp

le a

nsw

er: T

he

cost

of

two

S

amp

le a

nsw

er: T

he

cost

of

thre

e ad

ult

’s t

icke

ts a

nd

4 c

hild

ren’

s

airl

ine

tick

ets

that

are

dis

cou

nte

d

tick

ets

to t

he

zoo

is $

38. H

ow

20

% is

$33

0. W

hat

is t

he

reg

ula

r m

uch

is a

n a

du

lt’s

tic

ket?

co

st o

f a

tick

et?

0.15

F =

N

T =

p +

(p

+ 7

)

16 m

i

29 m

i

1 −

4 (r

+ 1

0) =

r -

4

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

812

/22/

10

12:1

8 P

M

Lesson 2-1


NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

Wri

tin

g E

qu

ati

on

s

2-1

Cha

pte

r 2

9 G

lenc

oe A

lgeb

ra 1

1.H

OU

SES

Th

e ar

ea o

f th

e H

arts

tein

’s

kitc

hen

is

182

squ

are

feet

. Th

is i

s 20

% o

f th

e ar

ea o

f th

e fi

rst

floo

r of

th

eir

hou

se.

Let

F r

epre

sen

t th

e ar

ea o

f th

e fi

rst

floo

r. W

rite

an

equ

atio

n t

o re

pres

ent

the

situ

atio

n.

2. F

AM

ILY

Kat

ie i

s tw

ice

as o

ld a

s h

er

sist

er M

ara.

Th

e su

m o

f th

eir

ages

is

24.

Wri

te a

on

e-va

riab

le e

quat

ion

to

repr

esen

t th

e si

tuat

ion

.

3. G

EOM

ETRY

Th

e fo

rmu

la F

+ V

=

E +

2 s

how

s th

e re

lati

onsh

ip b

etw

een

th

e n

um

ber

of f

aces

F, e

dges

E, a

nd

vert

ices

V o

f a

poly

hed

ron

, su

ch a

s a

pyra

mid

. Wri

te t

he

form

ula

in

wor

ds.

Face

Verte

xEd

ge

4. W

IREL

ESS

PHO

NE

Spi

nfr

og w

irel

ess

phon

e co

mpa

ny

bill

s on

a m

onth

ly b

asis

. E

ach

bil

l in

clu

des

a $2

9.95

ser

vice

fee

for

10

00 m

inu

tes

plu

s a

$2.9

5 fe

dera

l co

mm

un

icat

ion

tax

. Add

itio

nal

ly, t

her

e is

a

char

ge o

f $0

.05

for

each

min

ute

use

d ov

er 1

000.

Let

m r

epre

sen

t th

e n

um

ber

of m

inu

tes

over

100

0 u

sed

duri

ng

the

mon

th. W

rite

an

equ

atio

n t

o de

scri

be t

he

cost

p o

f th

e w

irel

ess

phon

e se

rvic

e pe

r m

onth

.

5. T

EMPE

RA

TUR

E T

he

tabl

e be

low

sh

ows

the

tem

pera

ture

in

Fah

ren

hei

t fo

r so

me

corr

espo

ndi

ng

tem

pera

ture

s in

Cel

siu

s.

Cel

siu

sFa

hre

nh

eit

-20

°-

4°

-10

°14

°

0°32

°

10°

50°

20°

68°

30°

86°

a. W

rite

a f

orm

ula

for

con

vert

ing

Cel

siu

s te

mpe

ratu

res

to F

ahre

nh

eit

tem

pera

ture

s.

b

. F

ind

the

Fah

ren

hei

t eq

uiv

alen

ts f

or

25ºC

an

d 35

ºC.

1

82 =

0.2

F

m

+ 2

m =

24

or

3m =

24

T

he

sum

of

the

nu

mb

er o

f fa

ces

and

nu

mb

er o

f ve

rtic

es is

eq

ual

to

th

e su

m o

f tw

o a

nd

th

e n

um

ber

of

edg

es.

p

= 3

2.90

+ 0

.05m

F

= 1

.8C

+ 3

2

77ºF

an

d

95ºF

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

912

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-1

Cha

pte

r 2

10

Gle

ncoe

Alg

ebra

1

Gu

ess t

he N

um

ber

Th

ink

of a

nu

mbe

r. A

dd f

ive

to y

our

nu

mbe

r. N

ow, d

oubl

e yo

ur

resu

lt. D

oubl

e yo

ur

resu

lt

agai

n. D

ivid

e yo

u a

nsw

er b

y fo

ur.

Fin

ally

, su

btra

ct y

our

orig

inal

nu

mbe

r. Yo

ur

resu

lt i

s fi

ve.

How

is

it p

ossi

ble

to k

now

wh

at t

he

answ

er i

s w

ith

out

know

ing

the

orig

inal

nu

mbe

r? W

rite

th

e st

eps

list

ed a

bove

as

an e

xpre

ssio

n i

n e

quat

ion

for

m. T

hen

use

alg

ebra

to

show

wh

y th

is

tric

k w

orks

.

Th

ink

of a

nu

mbe

r:

x

Add

fiv

e to

you

r n

um

ber:

x

+ 5

Dou

ble

you

r re

sult

: 2(

x +

5)

Dou

ble

you

r re

sult

aga

in:

2(2(

x +

5))

Div

ide

you

an

swer

by

fou

r:

2(2(

x +

5))

−

4

Su

btra

ct y

our

orig

inal

nu

mbe

r:

2(2(

x +

5))

−

4

- x

Sim

plif

y th

e fi

nal

exp

ress

ion

: 4

(x +

5)

−

4

- x

M

ultip

ly.

x +

5 -

x

D

ivid

e.

5

Sim

plify

.

So,

th

e re

sult

wil

l al

way

s be

fiv

e, n

o m

atte

r w

hat

th

e st

arti

ng

nu

mbe

r is

.

Wri

te v

aria

ble

exp

ress

ion

s to

det

erm

ine

wh

y ea

ch n

um

ber

tri

ck w

ork

s.

1. T

hin

k of

a n

um

ber.

Add

eig

ht.

Dou

ble

you

r re

sult

. Nex

t, s

ubt

ract

16.

Fin

ally

, div

ide

you

r re

sult

by

2. Y

ou g

et y

our

orig

inal

nu

mbe

r ba

ck.

2. T

hin

k of

a n

um

ber.

Mu

ltip

ly b

y 10

. Add

5 t

o yo

ur

resu

lt. N

ext,

su

btra

ct 3

. Th

en a

dd 2

. N

ext,

su

btra

ct 4

. Div

ide

you

r re

sult

by

5. F

inal

ly, s

ubt

ract

you

r or

igin

al n

um

ber.

You

r re

sult

is

you

r or

igin

al n

um

ber.

3. T

hin

k of

a n

um

ber.

Add

1. M

ult

iply

you

r re

sult

by

6. N

ow, d

oubl

e yo

ur

resu

lt. N

ext,

di

vide

you

r re

sult

by

12. F

inal

ly, s

ubt

ract

you

r or

igin

al n

um

ber.

You

r re

sult

is

1.

4. T

hin

k of

a n

um

ber.

Mu

ltip

ly b

y 5.

Add

fiv

e to

you

r re

sult

. Now

, div

ide

by 5

. Su

btra

ct 1

fr

om y

our

resu

lt. F

inal

ly, s

ubt

ract

you

r or

igin

al n

um

ber.

You

r fi

nal

res

ult

is

0.

5. T

hin

k of

a n

um

ber.

Add

30.

Mu

ltip

ly b

y 3.

Mu

ltip

ly a

gain

by

2. D

ivid

e yo

ur

resu

lt b

y 6.

F

inal

ly, s

ubt

ract

you

r or

igin

al n

um

ber.

You

r an

swer

is

30.

2(6(

x +

1))

−

12

-

x =

1

(5x +

5)

−

5

- 1

- x

= 0

(2(x

+ 8

) -

16)

−

2

= x

2(3(

x +

30)

)

−

6

- x

= 3

0

(10x

+ 5

- 3

+ 2

- 4

)

−−

5

- x

= x

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1012

/22/

10

12:1

8 P

M

Lesson 2-2


NA

ME

DAT

E

P

ER

IOD

Lesson 2-2

2-2

Stud

y G

uide

and

Inte

rven

tion

S

olv

ing

On

e-S

tep

Eq

uati

on

s

Cha

pte

r 2

11

Gle

ncoe

Alg

ebra

1

Solv

e Eq

uat

ion

s U

sin

g A

dd

itio

n a

nd

Su

btr

acti

on

If

the

sam

e n

um

ber

is a

dded

to

eac

h s

ide

of a

n e

quat

ion

, th

e re

sult

ing

equ

atio

n i

s eq

uiv

alen

t to

th

e or

igin

al o

ne.

In

ge

ner

al i

f th

e or

igin

al e

quat

ion

in

volv

es s

ubt

ract

ion

, th

is p

rope

rty

wil

l h

elp

you

sol

ve t

he

equ

atio

n. S

imil

arly

, if

the

sam

e n

um

ber

is s

ubt

ract

ed f

rom

eac

h s

ide

of a

n e

quat

ion

, th

e re

sult

ing

equ

atio

n i

s eq

uiv

alen

t to

th

e or

igin

al o

ne.

Th

is p

rope

rty

wil

l h

elp

you

sol

ve

equ

atio

ns

invo

lvin

g ad

diti

on.

Ad

dit

ion

Pro

per

ty o

f E

qu

alit

yF

or a

ny n

umbe

rs a

, b

, an

d c,

if a

= b

, th

en a

+ c

= b

+ c

.

Su

btr

acti

on

Pro

per

ty o

f E

qu

alit

yF

or a

ny n

umbe

rs a

, b

, an

d c,

if a

= b

, th

en a

- c

= b

- c

.

S

olve

m -

32

= 1

8.

m

- 3

2 =

18

Orig

inal

equ

atio

n

m -

32

+ 3

2 =

18

+ 3

2 A

dd 3

2 to

eac

h si

de.

m

= 5

0 S

impl

ify.

Th

e so

luti

on i

s 50

.

S

olve

22

+ p

= -

12.

2

2 +

p =

-12

O

rigin

al e

quat

ion

22 +

p -

22

= -

12 -

22

Sub

trac

t 22

fro

m e

ach

side

.

p

= -

34

Sim

plify

.

Th

e so

luti

on i

s -

34.

Exe

rcis

esS

olve

eac

h e

qu

atio

n. C

hec

k y

our

solu

tion

.

1. h

- 3

= -

2

2. m

- 8

= -

12

3. p

- 5

= 1

5

4. 2

0 =

y -

8

5. k

- 0

.5 =

2.3

6.

w -

1 −

2 =

5 −

8

7. h

- 1

8 =

-17

8.

-12

= -

24 +

k

9. j

- 0

.2 =

1.8

10. b

- 4

0 =

-40

11

. m -

(-

12)

= 1

0

12. w

- 3 −

2 =

1 −

4

13. x

+ 1

2 =

6

14. w

+ 2

= -

13

15. -

17 =

b +

4

16. k

+ (

-9)

= 7

17

. -3.

2 =

� +

(-

0.2)

18

. - 3 −

8 +

x =

5 −

8

19. 1

9 +

h =

-4

20

. -12

= k

+ 2

4

21. j

+ 1

.2 =

2.8

22. b

+ 8

0 =

-80

23

. m +

(-

8) =

2

24. w

+ 3 −

2 =

5 −

8

Exam

ple

2Ex

amp

le 1

1 28

1 0

-6 16

-23

-16

0

-4

2.8 12 -

2

-15

-3

-36

10

20 1 1 −

8 2

7 −

4 -21

1 1.6

- 7 −

8

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1112

/22/

10

12:1

8 P

M

Answers (Lesson 2-1 and Lesson 2-2)


An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

So

lvin

g O

ne-S

tep

Eq

uati

on

s

2-2

Cha

pte

r 2

12

Gle

ncoe

Alg

ebra

1

Solv

e Eq

uat

ion

s U

sin

g M

ult

iplic

atio

n a

nd

Div

isio

n I

f ea

ch s

ide

of a

n e

quat

ion

is

mu

ltip

lied

by

the

sam

e n

um

ber,

the

resu

ltin

g eq

uat

ion

is

equ

ival

ent

to t

he

give

n o

ne.

You

ca

n u

se t

he

prop

erty

to

solv

e eq

uat

ion

s in

volv

ing

mu

ltip

lica

tion

an

d di

visi

on. T

o so

lve

equ

atio

ns

wit

h m

ult

ipli

cati

on a

nd

divi

sion

, you

can

als

o u

se t

he

Div

isio

n P

rope

rty

of

Equ

alit

y. I

f ea

ch s

ide

of a

n e

quat

ion

is

divi

ded

by t

he

sam

e n

um

ber,

the

resu

ltin

g eq

uat

ion

is

tru

e.

Mu

ltip

licat

ion

Pro

per

ty o

f E

qu

alit

yF

or a

ny n

umbe

rs a

, b

, an

d c,

if a

= b

, th

en a

c =

bc.

Div

isio

n P

rop

erty

of

Eq

ual

ity

For

any

num

bers

a,

b,

and

c, w

ith c

≠ 0

, if

a =

b,

then

a −

c =

b

−

c .

S

olve

3 1 −

2 p =

1 1 −

2 .

3

1 −

2 p

= 1

1 −

2

Orig

inal

equ

atio

n

7 −

2 p

= 3 −

2

2 −

7 ( 7

−

2 p) =

2 −

7 ( 3

−

2 ) M

ultip

ly e

ach

side

by

2 −

7 .

p

= 3 −

7

Sim

plify

.

Th

e so

luti

on i

s 3 −

7 .

S

olve

-5n

= 6

0.

-

5n =

60

Orig

inal

equ

atio

n

-5n

−

-5

= 6

0 −

-

5 D

ivid

e ea

ch s

ide

by -

5.

n

= -

12

Sim

plify

.

Th

e so

luti

on i

s -

12.

Exer

cise

sS

olve

eac

h e

qu

atio

n. C

hec

k y

our

solu

tion

.

1.

h

−

3 = -

2

2. 1 −

8 m

= 6

3.

1 −

5 p

= 3 −

5

4. 5

=

y −

12

5.

- 1 −

4 k

= -

2.5

6.

- m

−

8 =

5 −

8

7. -

1 1 −

2 h

= 4

8.

-12

= -

3 −

2 k

9.

j −

3 =

2 −

5

10. -

3 1 −

3 b

= 5

11

. 7 −

10

m =

10

12

. p −

5 =

- 1 −

4

13. 3

h =

-42

14

. 8m

= 1

6

15. -

3t =

51

16. -

3r =

-24

17

. 8k

= -

64

18. -

2m =

16

19. 1

2h =

4

20. -

2.4p

= 7

.2

21. 0

.5j

= 5

22. -

25 =

5m

23

. 6m

= 1

5

24. -

1.5p

= -

75

Exam

ple

2Ex

amp

le 1

Rew

rite

each

mix

ed n

umbe

r as

an

impr

oper

fra

ctio

n.

-6

483

6010

-

5

-8

−

3 8

1 1 −

5

-1

1 −

2

14 2 −

7

-1

1 −

4

-14 8

1 −

3

-5

2 -8

-17

-8

-3

10

502

1 −

2

001_

012_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1212

/22/

10

12:1

8 P

M

Lesson 2-2


NA

ME

DAT

E

P

ER

IOD

2-2

Skill

s Pr

acti

ceS

olv

ing

On

e-S

tep

Eq

uati

on

s

Cha

pte

r 2

13

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

1. y

- 7

= 8

2.

w +

14

= -

8

3. p

- 4

= 6

4.

-13

= 5

+ x

5. 9

8 =

b +

34

6.

y -

32

= -

1

7. n

+ (

-28

) =

0

8. y

+ (

-10

) =

6

9. -

1 =

t +

(-

19)

10

. j -

(-

17)

= 3

6

11. 1

4 =

d +

(-

10)

12

. u +

(-

5) =

-15

13. 1

1 =

-16

+ y

14

. c -

(-

3) =

100

15. 4

7 =

w -

(-

8)

16. x

- (

-74

) =

-22

17. 4

- (

-h

) =

68

18

. -56

= 2

0 -

(-

j)

19. 1

2z =

108

20

. -7t

= 4

9

21. 1

8f =

-21

6

22. -

22 =

11v

23. -

6d =

-42

24

. 96

= -

24a

25.

c −

4 =

16

26

. a −

16

= 9

27. -

84 =

d

−

3 28

. - d

−

7 =

-13

29.

t −

4 =

-13

30

. 31

= -

1 −

6 n

31. -

6 =

2 −

3 z

32

. 2 −

7 q

= -

4

33.

5 −

9 p

= -

10

34.

a −

10 =

2 −

5

15 10

64

28

18 24

27 39 64

9 -12

-22

-18

31 16 19 -10

97

-96

-76

-7

-2

7-

4

6414

4

-25

291

-52

-18

6

-9

-14

-18

4

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1312

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Prac

tice

So

lvin

g O

ne-S

tep

Eq

uati

on

s

2-2

Cha

pte

r 2

14

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

1. d

- 8

= 1

7

2. v

+ 1

2 =

-5

3.

b -

2 =

-11

4. -

16 =

m +

71

5.

29

= a

- 7

6

6. -

14 +

y =

-2

7. 8

- (

-n

) =

1

8. 7

8 +

r =

-15

9.

f +

(-

3) =

-9

10. 8

j =

96

11

. -13

z =

-39

12

. -18

0 =

15m

13. 2

43 =

27r

14

. y −

9 =

-8

15

. - j

−

12 =

-8

16.

a −

15 =

4 −

5

17.

g −

27

= 2 −

9

18.

q −

24

= 1 −

6

Wri

te a

n e

qu

atio

n f

or e

ach

sen

ten

ce. T

hen

sol

ve t

he

equ

atio

n.

19. N

egat

ive

nin

e ti

mes

a n

um

ber

equ

als

-11

7.

20. N

egat

ive

one

eigh

th o

f a

nu

mbe

r is

- 3 −

4 .

21. F

ive

sixt

hs

of a

nu

mbe

r is

- 5 −

9 .

22. 2

.7 t

imes

a n

um

ber

equ

als

8.37

.

23. H

UR

RIC

AN

ES T

he

day

afte

r a

hu

rric

ane,

th

e ba

rom

etri

c pr

essu

re i

n a

coa

stal

tow

n h

as

rise

n t

o 29

.7 i

nch

es o

f m

ercu

ry, w

hic

h i

s 2.

9 in

ches

of

mer

cury

hig

her

th

an t

he

pres

sure

w

hen

th

e ey

e of

th

e h

urr

ican

e pa

ssed

ove

r.

a.

Wri

te a

n a

ddit

ion

equ

atio

n t

o re

pres

ent

the

situ

atio

n.

b

. Wh

at w

as t

he

baro

met

ric

pres

sure

wh

en t

he

eye

pass

ed o

ver?

24. R

OLL

ER C

OA

STER

S K

ingd

a K

a in

New

Jer

sey

is t

he

tall

est

and

fast

est

roll

er c

oast

er i

n

the

wor

ld. R

ider

s tr

avel

at

an a

vera

ge s

peed

of

61 f

eet

per

seco

nd

for

3118

fee

t. T

hey

re

ach

a m

axim

um

spe

ed o

f 18

7 fe

et p

er s

econ

d.

a.

If

x re

pres

ents

th

e to

tal

tim

e th

at t

he

roll

er c

oast

er i

s in

mot

ion

for

eac

h r

ide,

w

rite

an

exp

ress

ion

to

repr

esen

t th

e si

tati

on.

(Hin

t: U

se t

he

dist

ance

fo

rmu

la d

= r

t.)

b

. How

lon

g is

th

e ro

ller

coa

ster

in

mot

ion

?

25-

17-

9

-87

105

12

-7

-93

-6

123

-12

9-

7296

-9n

= -

117;

13

- 1 −

8 n

= -

3 −

4 ;

6 b +

2.9

= 2

9.7

26.8

in. o

f m

ercu

ry

126

4

61x =

311

8

51.1

sec

on

ds

5 −

6 n

= -

5 −

9 ;

- 2 −

3

2.7

n =

8.3

7; 3

.1

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1412

/22/

10

12:1

8 P

M

Lesson 2-2


NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

So

lvin

g O

ne-S

tep

Eq

uati

on

s

2-2

Cha

pte

r 2

15

Gle

ncoe

Alg

ebra

1

1. S

UPR

EME

CO

UR

T C

hief

Jus

tice

W

illi

am R

ehnq

uist

ser

ved

on t

he

Sup

rem

e C

ourt

for

33

year

s un

til h

is

deat

h in

200

5. W

rite

and

sol

ve a

n

equa

tion

to

dete

rmin

e th

e ye

ar h

e w

as

conf

irm

ed a

s a

just

ice

on t

he S

upre

me

Cou

rt.

2. S

ALA

RY I

n a

rec

ent

year

, th

e an

nu

al

sala

ry o

f th

e G

over

nor

of

New

Yor

k w

as

$179

,000

. Du

rin

g th

e sa

me

year

, th

e an

nu

al s

alar

y of

th

e G

over

nor

of

Ten

nes

see

was

$94

,000

les

s. W

rite

an

d so

lve

an e

quat

ion

it

to f

ind

the

ann

ual

sa

lary

of

the

Gov

ern

or o

f Ten

nes

see

in

that

yea

r.

3. W

EATH

ER O

n a

col

d Ja

nu

ary

day,

M

avis

not

iced

th

at t

he

tem

pera

ture

dr

oppe

d 21

deg

rees

ove

r th

e co

urs

e of

th

e da

y to

–9º

C. W

rite

an

d so

lve

an e

quat

ion

to

det

erm

ine

wh

at t

he

tem

pera

ture

was

at

th

e be

gin

nin

g of

th

e da

y.

4. F

AR

MIN

G M

r. H

ill’s

far

m i

s 12

6 ac

res.

M

r. H

ill’s

far

m i

s 1 − 4 t

he

size

of

Mr.

Mil

ler’

s fa

rm. H

ow m

any

acre

s is

M

r. M

ille

r’s

farm

?

5. N

AU

TIC

AL

On

th

e se

a, d

ista

nce

s ar

e m

easu

red

in n

auti

cal

mil

es r

ath

er t

han

m

iles

.

a.

If

a bo

at t

rave

ls 1

6 kn

ots

in 1

hou

r, h

ow f

ar w

ill

it h

ave

trav

eled

in

fee

t?

Wri

te a

nd

solv

e an

equ

atio

n.

b

. A

bou

t h

ow f

ast

was

th

e bo

at t

rave

lin

g in

mil

es p

er h

our?

Rou

nd

you

r an

swer

to

th

e n

eare

st h

un

dred

th.

1 na

utic

al m

ile =

608

0 fe

et

1 kn

ot =

1

naut

ical

mile

−

ho

ur

2

005

- x

= 3

3; x

= 1

972

1

79,0

00

- 9

4,0

00

= s

or

179,

00

0 -

s =

94,

00

0;

s =

$85

,00

0

x

- 2

1 =

-9;

x =

12º

C

504

acre

s

6080

× 1

6 =

x;

x =

97,

280

ft

97,2

80 ÷

528

0 =

18.

42 m

ph

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1512

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-2

Cha

pte

r 2

16

Gle

ncoe

Alg

ebra

1

Ele

vato

r P

uzzle

José

get

s on

th

e el

evat

or a

nd

ride

s w

ith

out

push

ing

any

butt

ons.

Fir

st, t

he

elev

ator

goe

s u

p 4

floo

rs w

her

e B

ob g

ets

on. B

ob g

oes

dow

n 6

flo

ors

and

gets

off

. At

that

sam

e fl

oor

Flo

ren

ce

gets

on

an

d go

es u

p on

e fl

oor

befo

re g

etti

ng

off.

Th

e el

evat

or t

hen

mov

es d

own

8 f

loor

s to

pi

ck u

p th

e H

artt

fam

ily

wh

o ri

de d

own

3 f

loor

s an

d ge

t of

f. T

hen

th

e el

evat

or g

oes

up

one

floo

r, pi

cks

up

Kri

s, a

nd

goes

dow

n 6

flo

ors

to t

he

stre

et l

evel

wh

ere

José

exi

ts t

he

elev

ator

.

1. S

upp

ose

x is

you

r st

arti

ng

poin

t. W

rite

an

equ

atio

n t

hat

rep

rese

nts

Jos

é’s

elev

ator

rid

e.

2. A

t w

hat

flo

or d

id J

osé

get

on t

he

elev

ator

?

Now

th

at y

ou k

now

th

e st

arti

ng

poi

nt

of J

osé,

th

e st

arti

ng

poi

nt

of e

very

oth

er

per

son

wh

o ro

de

the

elev

ator

can

be

det

erm

ined

.

3. A

t w

hat

flo

or d

id B

ob g

et o

n t

he

elev

ator

? A

t w

hat

flo

or d

id B

ob g

et o

ff?

4. A

t w

hat

flo

or d

id F

lore

nce

get

on

th

e el

evat

or?

At

wh

at f

loor

did

Flo

ren

ce g

et o

ff?

5. A

t w

hat

flo

or d

id t

he

Har

tt f

amil

y ge

t on

th

e el

evat

or?

At

wh

at f

loor

did

th

e H

artt

fa

mil

y ge

t of

f?

6. A

t w

hat

flo

or d

id K

ris

get

on t

he

elev

ator

? A

t w

hat

flo

or d

id K

ris

get

off?

x +

4 -

6 +

1 -

8 -

3 +

1 -

6 =

0

17th

fl o

or

21st

fl o

or;

15t

h fl

oo

r

15th

fl o

or;

16t

h fl

oo

r

8th

fl o

or;

5th

fl o

or

6th

fl o

or;

str

eet

leve

l fl o

or

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1612

/22/

10

12:1

8 P

M

Lesson 2-3


NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

So

lvin

g M

ult

i-S

tep

Eq

uati

on

s

2-3

Cha

pte

r 2

17

Gle

ncoe

Alg

ebra

1

Wo

rk B

ackw

ard

Wor

kin

g b

ack

war

d i

s on

e of

man

y pr

oble

m-s

olvi

ng

stra

tegi

es t

hat

yo

u c

an u

se t

o so

lve

prob

lem

s. T

o w

ork

back

war

d, s

tart

wit

h t

he

resu

lt g

iven

at

the

end

of a

pr

oble

m a

nd

un

do e

ach

ste

p to

arr

ive

at t

he

begi

nn

ing

nu

mbe

r.

A

nu

mb

er i

s d

ivid

ed

by

2, a

nd

th

en 8

is

sub

trac

ted

fro

m

the

qu

otie

nt.

Th

e re

sult

is

16. W

hat

is

th

e n

um

ber

?S

olve

the

pro

blem

by

wor

king

bac

kwar

d.

Th

e fi

nal

nu

mbe

r is

16.

Un

do

subt

ract

ing

8 by

add

ing

8 to

get

24.

To

un

do d

ivid

ing

24 b

y 2,

mu

ltip

ly 2

4 by

2

to g

et 4

8.

Th

e or

igin

al n

um

ber

is 4

8.

A

bac

teri

a cu

ltu

re d

oub

les

each

hal

f h

our.

Aft

er 3

hou

rs, t

her

e ar

e 64

00 b

acte

ria.

How

man

y b

acte

ria

wer

e th

ere

to b

egin

wit

h?

Sol

ve t

he

prob

lem

by

wor

kin

g ba

ckw

ard.

Th

e ba

cter

ia h

ave

grow

n f

or 3

hou

rs. S

ince

th

ere

are

2 on

e-ha

lf h

our

peri

ods

in o

ne h

our,

in 3

hou

rs

ther

e ar

e 6

one-

hal

f h

our

peri

ods.

Sin

ce t

he

bact

eria

cu

ltu

re h

as g

row

n f

or 6

tim

e pe

riod

s, i

t h

as d

oubl

ed 6

tim

es. U

ndo

th

e do

ubl

ing

by

hal

vin

g th

e n

um

ber

of b

acte

ria

6 ti

mes

.

6400

× 1 −

2 ×

1 −

2 ×

1 −

2 ×

1 −

2 ×

1 −

2 ×

1 −

2 =

640

0 ×

1 −

64

=

100

Th

ere

wer

e 10

0 ba

cter

ia t

o be

gin

wit

h.

Exer

cise

sS

olve

eac

h p

rob

lem

by

wor

kin

g b

ack

war

d.

1. A

nu

mbe

r is

div

ided

by

3, a

nd

then

4 i

s ad

ded

to t

he

quot

ien

t. T

he

resu

lt i

s 8.

Fin

d th

e n

um

ber.

2. A

nu

mbe

r is

mu

ltip

lied

by

5, a

nd

then

3 i

s su

btra

cted

fro

m t

he

prod

uct

. Th

e re

sult

is

12.

Fin

d th

e n

um

ber.

3. E

igh

t is

su

btra

cted

fro

m a

nu

mbe

r, an

d th

en t

he

diff

eren

ce i

s m

ult

ipli

ed b

y 2.

Th

e re

sult

is

24.

Fin

d th

e n

um

ber.

4. T

hre

e ti

mes

a n

um

ber

plu

s 3

is 2

4. F

ind

the

nu

mbe

r.

5. C

AR

REN

TAL

An

gela

ren

ted

a ca

r fo

r $2

9.99

a d

ay p

lus

a on

e-ti

me

insu

ran

ce c

ost

of

$5.0

0. H

er b

ill

was

$12

4.96

. For

how

man

y da

ys d

id s

he

ren

t th

e ca

r?

6. M

ON

EY M

ike

wit

hdr

ew a

n a

mou

nt

of m

oney

fro

m h

is b

ank

acco

un

t. H

e sp

ent

one

fou

rth

for

gas

olin

e an

d h

ad $

90 l

eft.

How

mu

ch m

oney

did

he

wit

hdr

aw?

Exam

ple

2Ex

amp

le 1

12

3

20

7

4 d

ays

$120

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1712

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

So

lvin

g M

ult

i-S

tep

Eq

uati

on

s

2-3

Cha

pte

r 2

18

Gle

ncoe

Alg

ebra

1

Solv

e M

ult

i-St

ep E

qu

atio

ns

To

solv

e eq

uat

ion

s w

ith

mor

e th

an o

ne

oper

atio

n, o

ften

ca

lled

mu

lti-

step

eq

uat

ion

s, u

ndo

ope

rati

ons

by w

orki

ng

back

war

d. R

ever

se t

he

usu

al

orde

r of

ope

rati

ons

as y

ou w

ork.

S

olve

5x

+ 3

= 2

3.

5x

+ 3

= 2

3 O

rigin

al e

quat

ion

5x +

3 -

3 =

23

- 3

S

ubtr

act

3 fr

om e

ach

side

.

5x

= 2

0 S

impl

ify.

5x

−

5

= 20

−

5

Div

ide

each

sid

e by

5.

x

= 4

S

impl

ify.

Exer

cise

sS

olve

eac

h e

qu

atio

n. C

hec

k y

our

solu

tion

.

1. 5

x +

2 =

27

2.

6x

+ 9

= 2

7

3. 5

x +

16

= 5

1

4. 1

4n -

8 =

34

5.

0.6

x -

1.5

= 1

.8

6. 7 −

8 p

- 4

= 1

0

7. 1

6 =

d -

12

−

14

8.

8 +

3n

−

12 =

13

9.

g

−

-5 +

3 =

-13

10.

4b +

8

−

-2

= 1

0

11. 0

.2x

- 8

= -

2

12. 3

.2y

- 1

.8 =

3

13. -

4 =

7x

- (

-1)

−

-8

14

. 8 =

-12

+

k −

-

4 15

. 0 =

10y

- 4

0

Wri

te a

n e

qu

atio

n a

nd

sol

ve e

ach

pro

ble

m.

16. F

ind

thre

e co

nse

cuti

ve i

nte

gers

wh

ose

sum

is

96.

17. F

ind

two

con

secu

tive

odd

in

tege

rs w

hos

e su

m i

s 17

6.

18. F

ind

thre

e co

nse

cuti

ve i

nte

gers

wh

ose

sum

is

-93

.

Exam

ple

53

7

35.

516

236

2080

-7

301.

5

4 3 −

7 -

804

n

+ (

n +

1)

+ (

n +

2)

= 9

6; 3

1, 3

2, 3

3

n

+ (

n +

2)

= 1

76;

87, 8

9

n

+ (

n +

1)

+ (

n +

2)

= -

93;

-32

, -31

, -30

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1812

/22/

10

12:1

8 P

M

Lesson 2-3


NA

ME

DAT

E

P

ER

IOD

Skill

s Pr

acti

ceS

olv

ing

Mu

lti-

Ste

p E

qu

ati

on

s

2-3

Cha

pte

r 2

19

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

pro

ble

m b

y w

ork

ing

bac

kw

ard

.

1. A

nu

mbe

r is

div

ided

by

2, a

nd

then

th

e qu

otie

nt

is a

dded

to

8. T

he

resu

lt i

s 33

.F

ind

the

nu

mbe

r.

2. T

wo

is s

ubt

ract

ed f

rom

a n

um

ber,

and

then

th

e di

ffer

ence

is

divi

ded

by 3

.T

he

resu

lt i

s 30

. Fin

d th

e n

um

ber.

3. A

nu

mbe

r is

mu

ltip

lied

by

2, a

nd

then

th

e pr

odu

ct i

s ad

ded

to 9

. Th

e re

sult

is

49.

Wh

at i

s th

e n

um

ber?

4. A

LLO

WA

NC

E A

fter

Ric

ardo

rec

eive

d h

is a

llow

ance

for

th

e w

eek,

he

wen

t to

th

e m

all

wit

h s

ome

frie

nds

. He

spen

t h

alf

of h

is a

llow

ance

on

a n

ew p

aper

back

boo

k. T

hen

he

bou

ght

him

self

a s

nac

k fo

r $1

.25.

Wh

en h

e ar

rive

d h

ome,

he

had

$5.

00 l

eft.

How

mu

ch

was

his

all

owan

ce?

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

5. 5

x +

3 =

23

6.

4 =

3a

- 1

4

7. 2

y +

5 =

19

8. 6

+ 5

c =

-29

9.

8 -

5w

= -

37

10. 1

8 -

4v

= 4

2

11.

n

−

3 - 8

= -

2

12. 5

+ x −

4 =

1

13. -

h

−

3 - 4

= 1

3

14. -

d

−

6 + 1

2 =

-7

15

. a −

5 -

2 =

9

16.

w

−

7 + 3

= -

1

17.

3 −

4 q

- 7

= 8

18

. 2 −

3 g

+ 6

= -

12

19.

5 −

2 z

- 8

= -

3

20.

4 −

5 m

+ 2

= 6

21

. c

- 5

−

4 =

3

22.

b +

1

−

3 =

2

Wri

te a

n e

qu

atio

n a

nd

sol

ve e

ach

pro

ble

m.

23. T

wic

e a

nu

mbe

r pl

us

fou

r eq

ual

s 6.

Wh

at i

s th

e n

um

ber?

24. S

ixte

en i

s se

ven

plu

s th

ree

tim

es a

nu

mbe

r. F

ind

the

nu

mbe

r.

25. F

ind

two

con

secu

tive

in

tege

rs w

hos

e su

m i

s 35

.

26. F

ind

thre

e co

nse

cuti

ve i

nte

gers

wh

ose

sum

is

36.

50

92

20

$12.

50

46

7

-7

9-

6

18-

16-

51

114

55-

28

20-

272

517

5

2n +

4 =

6;

1

16 =

7 +

3n

; 3

n +

(n

+ 1

) =

35;

17,

18

n +

(n

+ 1

) +

(n

+ 2

) =

36;

11

, 12,

13

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

1912

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Prac

tice

So

lvin

g M

ult

i-S

tep

Eq

uati

on

s

2-3

Cha

pte

r 2

20

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

pro

ble

m b

y w

ork

ing

bac

kw

ard

.

1. T

hre

e is

add

ed t

o a

nu

mbe

r, an

d th

en t

he

sum

is

mu

ltip

lied

by

4. T

he

resu

lt i

s 16

. Fin

d th

e n

um

ber.

2. A

nu

mbe

r is

div

ided

by

4, a

nd

the

quot

ien

t is

add

ed t

o 3.

Th

e re

sult

is

24. W

hat

is

the

nu

mbe

r?

3. T

wo

is s

ubt

ract

ed f

rom

a n

um

ber,

and

then

th

e di

ffer

ence

is

mu

ltip

lied

by

5. T

he

resu

lt

is 3

0. F

ind

the

nu

mbe

r.

4. B

IRD

WA

TCH

ING

Wh

ile

Mic

hel

le s

at o

bser

vin

g bi

rds

at a

bir

d fe

eder

, on

e fo

urt

h o

f th

e bi

rds

flew

aw

ay w

hen

th

ey w

ere

star

tled

by

a n

oise

. Tw

o bi

rds

left

th

e fe

eder

to

go t

o an

oth

er s

tati

oned

a f

ew f

eet

away

. Th

ree

mor

e bi

rds

flew

in

to t

he

bran

ches

of

a n

earb

y tr

ee. F

our

bird

s re

mai

ned

at

the

feed

er. H

ow m

any

bird

s w

ere

at t

he

feed

er i

nit

iall

y?

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

5. -

12n

- 1

9 =

77

6.

17

+ 3

f =

14

7.

15t

+ 4

= 4

9

8.

u

−

5 + 6

= 2

9.

d

−

-4 +

3 =

15

10

. b −

3 -

6 =

-2

11.

1 −

2 y

- 1 −

8 =

7 −

8

12. -

32 -

3 −

5 f

= -

17

13. 8

- 3 −

8 k

= -

4

14.

r +

13

−

12

=

1

15.

15 -

a

−

3

= -

9

16.

3k -

7

−

5

= 1

6

17.

x −

7 -

0.5

= 2

.5

18. 2

.5g

+ 0

.45

= 0

.95

19

. 0.4

m -

0.7

= 0

.22

Wri

te a

n e

qu

atio

n a

nd

sol

ve e

ach

pro

ble

m.

20. S

even

les

s th

an f

our

tim

es a

nu

mbe

r eq

ual

s 13

. Wh

at i

s th

e n

um

ber?

21. F

ind

two

con

secu

tive

odd

in

tege

rs w

hos

e su

m i

s 11

6.

22. F

ind

two

con

secu

tive

eve

n i

nte

gers

wh

ose

sum

is

126.

23. F

ind

thre

e co

nse

cuti

ve o

dd i

nte

gers

wh

ose

sum

is

117.

24. C

OIN

CO

LLEC

TIN

G J

un

g h

as a

tot

al o

f 92

coi

ns

in h

is c

oin

col

lect

ion

. Th

is i

s 8

mor

e th

an t

hre

e ti

mes

th

e n

um

ber

of q

uar

ters

in

th

e co

llec

tion

. How

man

y qu

arte

rs d

oes

Jun

g h

ave

in h

is c

olle

ctio

n?

1

84

8

12

-8

-1

3

-20

-48

12

2-

2532

-1

4229

210.

22.

3

4n -

7 =

13;

5

n +

(n

+ 2

) =

116

; 57

, 59

n +

(n

+ 2

) =

126

; 62

, 64

n +

(n

+ 2

) +

(n

+ 4

) =

117

; 37

, 39,

41

28

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2012

/22/

10

12:1

8 P

M

Lesson 2-3


NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

So

lvin

g M

ult

i-S

tep

Eq

uati

on

s

2-3

Cha

pte

r 2

21

Gle

ncoe

Alg

ebra

1

1. T

EMPE

RA

TUR

E T

he

form

ula

for

co

nve

rtin

g a

Fah

ren

hei

t te

mpe

ratu

re t

o

a

Cel

siu

s te

mpe

ratu

re i

s C

=

F -

32º

−1.

8 .

F

ind

the

equ

ival

ent

Cel

siu

s te

mpe

ratu

re

fo

r 68

ºF.

2. H

UM

AN

HEI

GH

T It

is

a co

mm

only

use

d gu

idel

ine

that

for

th

e av

erag

e A

mer

ican

ch

ild,

th

eir

max

imu

m a

dult

hei

ght

wil

l be

abo

ut

twic

e th

eir

hei

ght

at a

ge 2

. S

upp

ose

that

Mic

ah’s

adu

lt h

eigh

t fi

ts

the

foll

owin

g eq

uat

ion

a =

2c

– 1,

wh

ere

a re

pres

ents

his

adu

lt h

eigh

t an

d c

repr

esen

ts h

is h

eigh

t at

age

2. A

t ag

e 2

Mic

ah w

as 3

5 in

ches

tal

l. W

hat

is

Mic

ah’s

adu

lt h

eigh

t? W

rite

an

d so

lve

an

equ

atio

n.

3. C

HEM

ISTR

Y T

he

hal

f-li

fe o

f a

radi

oact

ive

subs

tan

ce i

s th

e ti

me

requ

ired

for

hal

f of

a s

ampl

e to

un

derg

o ra

dioa

ctiv

e de

cay,

or

for

the

quan

tity

to

fall

to

hal

f it

s or

igin

al a

mou

nt.

Car

bon

14

has

a h

alf-

life

of

5730

yea

rs. S

upp

ose

gi

ven

sam

ples

of

carb

on 1

4 w

eigh

5 −

8 o

f

a po

un

d an

d 7 −

8 o

f a

pou

nd.

Wh

at w

as t

he

to

tal

wei

ght

of t

he

sam

ples

11,

460

year

s

ago?

4. N

UM

BER

TH

EORY

Wri

te a

nd

solv

e an

eq

uat

ion

to

fin

d th

ree

con

secu

tive

odd

in

tege

rs w

hos

e su

m i

s 3.

5. G

EOM

ETRY

A r

ecta

ngu

lar

swim

min

g po

ol i

s su

rrou

nde

d by

a c

oncr

ete

side

wal

k th

at i

s 3

feet

wid

e. T

he

dim

ensi

ons

of t

he

rect

angl

e cr

eate

d by

th

e si

dew

alk

are

21 f

eet

by 3

1 fe

et.

a.F

ind

the

len

gth

an

d w

idth

of

the

pool

.

b

. Fin

d th

e ar

ea o

f th

e po

ol.

c.

Wri

te a

nd

solv

e an

equ

atio

n t

o fi

nd

the

area

of

the

side

wal

k in

squ

are

feet

.

3 ft

31 ft

21 ft

pool

2

0ºC

a

= 2

c -

1;

c =

69

inch

es

w

= (

5 −

8 +

7 −

8 )

× 2

× 2

w

= 6

po

un

ds

n

+ (n

+ 2

) + (n

+ 4

) =

3

3n

+ 6

= 3

3n =

-3

n =

-1

n +

2 =

1

n

+ 4

= 3

ℓ

= 2

1 -

3 -

3

w =

31

- 3

- 3

ℓ

= 1

5 fe

et

w =

25

feet

A

= ℓ

. w

A

= 1

5 .

25

A

= 3

75 s

qu

are

feet

A

= ℓ

. w

- 3

75

A

= (

21 .

31)

- 3

75

A

= 6

51 -

375

A =

276

sq

uar

e fe

et

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2112

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-3

Cha

pte

r 2

22

Gle

ncoe

Alg

ebra

1

Co

nsecu

tive I

nte

ger

Pro

ble

ms

Man

y ty

pes

of p

robl

ems

and

puzz

les

invo

lve

the

idea

of

con

secu

tive

in

tege

rs. K

now

ing

how

to

repr

esen

t th

ese

inte

gers

alg

ebra

ical

ly c

an

hel

p to

sol

ve t

he

prob

lem

.

F

ind

fou

r co

nse

cuti

ve o

dd

in

tege

rs w

hos

e su

m i

s -

80.

An

odd

in

tege

r ca

n b

e w

ritt

en a

s 2n

+ 1

, wh

ere

n i

s an

y in

tege

r. If

2n

+ 1

is

the

firs

t od

d in

tege

r, th

en a

dd 2

to

get

the

nex

t la

rges

t od

d in

tege

r, an

d so

on

.N

ow w

rite

an

equ

atio

n t

o so

lve

this

pro

blem

.(2

n +

1)

+ (

2n +

3)

+ (

2n +

5)

+ (

2n +

7)

= -

80

Exer

cise

sW

rite

an

eq

uat

ion

for

eac

h p

rob

lem

. Th

en s

olve

.

1. C

ompl

ete

the

solu

tion

to

the

prob

lem

in

th

e ex

ampl

e.

2. F

ind

thre

e co

nse

cuti

ve e

ven

in

tege

rs w

hos

e su

m i

s 13

2.

3. F

ind

two

con

secu

tive

in

tege

rs w

hos

e su

m i

s 19

.

4. F

ind

two

con

secu

tive

in

tege

rs w

hos

e su

m i

s 10

0.

5. T

he

less

er o

f tw

o co

nse

cuti

ve e

ven

in

tege

rs i

s 10

mor

e th

an

one-

hal

f th

e gr

eate

r. F

ind

the

inte

gers

.

6. T

he

grea

ter

of t

wo

con

secu

tive

eve

n i

nte

gers

is

6 le

ss t

han

th

ree

tim

es t

he

less

er. F

ind

the

inte

gers

.

7. F

ind

fou

r co

nse

cuti

ve i

nte

gers

su

ch t

hat

tw

ice

the

sum

of

the

two

grea

ter

inte

gers

exc

eeds

th

ree

tim

es t

he

firs

t by

91.

8. F

ind

a se

t of

fou

r co

nse

cuti

ve p

osit

ive

inte

gers

su

ch t

hat

th

e gr

eate

st i

nte

ger

in t

he

set

is t

wic

e th

e le

ast

inte

ger

in t

he

set.

Exam

ple

-

23, -

21, -

19, -

17

2

n +

(2n

+ 2

) +

(2n

+ 4

) =

132

; n

= 2

1; 4

2, 4

4, 4

6

n

+ (

n +

1)

= 1

9; 9

, 10

n

+ (

n +

1)

= 1

00;

no

so

luti

on

2

n =

10

+ 1 −

2 (2n

+ 2

); 2

2 an

d 2

4

2

n +

2 =

3(2

n)

- 6

; 4,

6

2

[(n

+ 2

) +

(n

+ 3

)] =

3n

+ 9

1; 8

1, 8

2, 8

3, 8

4

n

+ 3

= 2

n;

3, 4

, 5, 6

013_

022_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2212

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-4

Stud

y G

uide

and

Inte

rven

tion

S

olv

ing

Eq

uati

on

s w

ith

th

e V

ari

ab

le o

n E

ach

Sid

e

2-4

Cha

pte

r 2

23

Gle

ncoe

Alg

ebra

1

Var

iab

les

on

Eac

h S

ide

To

solv

e an

equ

atio

n w

ith

th

e sa

me

vari

able

on

eac

h s

ide,

fi

rst

use

th

e A

ddit

ion

or

the

Su

btra

ctio

n P

rope

rty

of E

qual

ity

to w

rite

an

equ

ival

ent

equ

atio

n t

hat

has

th

e va

riab

le o

n ju

st o

ne

side

of

the

equ

atio

n. T

hen

sol

ve t

he

equ

atio

n.

S

olve

5y

- 8

= 3

y +

12.

5y

- 8

= 3

y +

12

5y -

8 -

3y

= 3

y +

12

- 3

y

2y -

8 =

12

2y

- 8

+ 8

= 1

2 +

8

2y =

20

2y

−

2 =

20

−

2

y

= 1

0

Th

e so

luti

on i

s 10

.

S

olve

-11

- 3

y =

8y

+ 1

.

-

11 -

3y

= 8

y +

1 -

11 -

3y

+ 3

y =

8y

+ 1

+ 3

y

-11

= 1

1y +

1

-11

- 1

= 1

1y +

1 -

1

-12

= 1

1y

-

12

−

11

= 11

y −

1

1

-

1 1 −

11

= y

Th

e so

luti

on i

s -

1 1 −

11

.

Exer

cise

sS

olve

eac

h e

qu

atio

n. C

hec

k y

our

solu

tion

.

1. 6

- b

= 5

b +

30

2. 5

y -

2y

= 3

y +

2

3. 5

x +

2 =

2x

- 1

0

4. 4

n -

8 =

3n

+ 2

5.

1.2

x +

4.3

= 2

.1 -

x

6. 4

.4m

+ 6

.2 =

8.8

m -

1.8

7.

1 −

2 b

+ 4

= 1 −

8 b

+ 8

8 8.

3 −

4 k

- 5

= 1 −

4 k

- 1

9.

8 -

5p

= 4

p -

1

10. 4

b -

8 =

10

- 2

b 11

. 0.2

x -

8 =

-2

- x

12

. 3y

- 1

.8 =

3y

- 1

.8

13. -

4 -

3x

= 7

x -

6

14. 8

+ 4

k =

-10

+ k

15

. 20

- a

= 1

0a -

2

16.

2 −

3 n

+ 8

= 1 −

2 n

+ 2

17

. 2 −

5 y

- 8

= 9

- 3 −

5 y

18

. -4r

+ 5

= 5

- 4

r

19. -

4 -

3x

= 6

x -

6

20. 1

8 -

4k

= -

10 -

4k

21. 1

2 +

2y

= 1

0y -

12

Exam

ple

1Ex

amp

le 2

-

4 n

o s

olu

tio

n

-4

1

0 -

1 20

−

11

2

24

8

1

3

5

a

ll n

um

ber

s

1

−

5 -

6 2

-

36

17

all

nu

mb

ers

2

−

9 n

o s

olu

tio

n

3

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2312

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

So

lvin

g E

qu

ati

on

s w

ith

th

e V

ari

ab

le o

n E

ach

Sid

e

2-4

Cha

pte

r 2

24

Gle

ncoe

Alg

ebra

1

Gro

up

ing

Sym

bo

ls W

hen

sol

vin

g eq

uat

ion

s th

at c

onta

in g

rou

pin

g sy

mbo

ls, f

irst

use

th

e D

istr

ibu

tive

Pro

pert

y to

eli

min

ate

grou

pin

g sy

mbo

ls. T

hen

sol

ve.

S

olve

4(2

a -

1)

= -

10(a

- 5

).

4(2

a -

1)

= -

10(a

- 5

) O

rigin

al e

quat

ion

8a

- 4

= -

10a

+ 5

0 D

istr

ibut

ive

Pro

pert

y

8a -

4 +

10a

= -

10a

+ 5

0 +

10a

A

dd 1

0a to

eac

h si

de.

18

a -

4 =

50

Sim

plify

.

18

a -

4 +

4 =

50

+ 4

A

dd 4

to e

ach

side

.

18

a =

54

Sim

plify

.

18a

−

18

= 54

−

18

D

ivid

e ea

ch s

ide

by 1

8.

a

= 3

S

impl

ify.

Th

e so

luti

on i

s 3.

Exer

cise

s S

olve

eac

h e

qu

atio

n. C

hec

k y

our

solu

tion

.

1. -

3(x

+ 5

) =

3(x

- 1

) 2.

2(7

+ 3

t) =

-t

3. 3

(a +

1)

- 5

= 3

a -

2

4. 7

5 -

9g

= 5

(-4

+ 2

g)

5. 5

(f +

2)

= 2

(3 -

f)

6. 4

(p +

3)

= 3

6

7. 1

8 =

3(2

t +

2)

8. 3

(d -

8)

= 3

d

9. 5

(p +

3)

+ 9

= 3

( p -

2)

+ 6

10. 4

(b -

2)

= 2

(5 -

b)

11. 1

.2(x

- 2

) =

2 -

x

12.

3 +

y

−

4 =

-y

−

8

13.

a -

8

−

12

= 2a

+ 5

−

3

14. 2

(4 +

2k)

+ 1

0 =

k

15. 2

(w -

1)

+ 4

= 4

(w +

1)

16. 6

(n -

1)

= 2

(2n

+ 4

) 17

. 2[2

+ 3

(y -

1)]

= 2

2 18

. -4(

r +

2)

= 4

(2 -

4r)

19. -

3(x

- 8

) =

24

20. 4

(4 -

4k)

= -

10 -

16k

21. 6

(2 -

2y)

= 5

(2y

- 2

)

Exam

ple

-

2 -

2 a

ll n

um

ber

s

5

-

4 −

7 6

2

n

o s

olu

tio

n

-12

3

2

-

2

-

4 -

6 -

1

7

4

1

1 −

3

0

n

o s

olu

tio

n

1

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2412

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-4

Skill

s Pr

acti

ceS

olv

ing

Eq

uati

on

s w

ith

th

e V

ari

ab

le o

n E

ach

Sid

e

2-4

Cha

pte

r 2

25

Gle

ncoe

Alg

ebra

1

Ju

stif

y ea

ch s

tep

.

1.

4k -

3 =

2k

+ 5

4

k -

3 -

2k

= 2

k +

5 -

2k

a.

2k -

3 =

5

b.

2k -

3 +

3 =

5 +

3

c.

2k =

8

d.

2k

−

2 =

8 −

2

e.

k =

4

f.

2.

2(8u

+ 2

) =

3(2

u -

7)

16u

+ 4

= 6

u -

21

a.

16u

+ 4

- 6

u =

6u

- 2

1 -

6u

b

.

10u

+ 4

= -

21

c.

10u

+ 4

- 4

= -

21 -

4

d.

10u

= -

25

e.

10u

−

10

= -

25

−

10

f.

u =

-2.

5 g.

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

3. 2

m +

12

= 3

m -

31

4.

2h

- 8

= h

+ 1

7

5. 7

a -

3 =

3 -

2a

6.

4n

- 1

2 =

12

- 4

n

7. 4

x -

9 =

7x

+ 1

2

8. -

6y -

3 =

3 -

6y

9. 5

+ 3

r =

5r

- 1

9

10. -

9 +

8k

= 7

+ 4

k

11. 8

q +

12

= 4

(3 +

2q)

12

. 3(5

j + 2

) = 2

(3j -

6)

13. 6

(-3v

+ 1

) = 5

(-2v

- 2

)

14. -

7(2b

- 4

) = 5

(-2b

+ 6

)

15. 3

(8 -

3t)

= 5

(2 +

t)

16

. 2(3

u +

7) =

-4(

3 -

2u)

17. 8

(2f -

2) =

7(3

f + 2

)

18. 5

(-6

- 3

d) =

3(8

+ 7

d)

19. 6

(w -

1) =

3(3

w +

5)

20

. 7(-

3y +

2) =

8(3

y -

2)

21.

2 −

3 v

- 6

= 6

- 2 −

3 v

22

. 1 −

2 -

5 −

8 x

= 7 −

8 x

+ 7 −

2

Su

btr

act

2k f

rom

eac

h s

ide.

Sim

plif

y.A

dd

3 t

o e

ach

sid

e.S

imp

lify.

Div

ide

each

sid

e by

2.

Sim

plif

y.

Dis

trib

uti

ve P

rop

erty

Su

btr

act

6u f

rom

eac

h s

ide.

Sim

plif

y.

Su

btr

act

4 fr

om

eac

h s

ide.

Sim

plif

y.

Div

ide

each

sid

e by

10.

Sim

plif

y.

4325

2 −

3

3

-7

no

so

luti

on

124

all n

um

ber

s-

2

2-

0.5

or

-

1 −

2

113

-6

-1.

5 o

r -

1 1 −

2

-7

2 −

3

9-

2

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2512

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Prac

tice

So

lvin

g E

qu

ati

on

s w

ith

th

e V

ari

ab

le o

n E

ach

Sid

e

2-4

Cha

pte

r 2

26

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

eq

uat

ion

. Ch

eck

you

r so

luti

on.

1. 5

x -

3 =

13

- 3

x

2. -

4r -

11

= 4

r +

21

3. 1

- m

= 6

- 6

m

4. 1

4 +

5n

= -

4n +

17

5.

1 −

2 k

- 3

= 2

- 3 −

4 k

6.

1 −

2 (

6 -

y) =

y

7. 3

(-2

- 3

x) =

-9x

- 4

8.

4(4

- w

) = 3

(2w

+ 2

)

9. 9

(4b

- 1

) = 2

(9b

+ 3

)

10. 3

(6 +

5y)

= 2

(-5

+ 4

y)

11. -

5x -

10

= 2

- (x

+ 4

)

12. 6

+ 2

(3j -

2) =

4(1

+ j)

13.

5 −

2 t

- t

= 3

+ 3 −

2 t

14

. 1.4

f + 1

.1 =

8.3

- f

15.

2 −

3 x

- 1 −

6 =

1 −

2 x

+ 5 −

6

16. 2

- 3 −

4 k

= 1 −

8 k

+ 9

17.

1 −

2 (3

g -

2) =

g −

2

18.

1 −

3 (n

+ 1

) = 1 −

6 (3

n -

5)

19.

1 −

2 (5

- 2

h) =

h −

2

20.

1 −

9 (

2m -

16)

= 1 −

3 (2

m +

4)

21. 3

(d -

8)

- 5

= 9

(d +

2)

+ 1

22

. 2(a

- 8

) + 7

= 5

(a +

2) -

3a

- 1

9

23. N

UM

BER

S T

wo

thir

ds o

f a n

umbe

r re

duce

d by

11

is e

qual

to

4 m

ore

than

the

num

ber.

Fin

d th

e nu

mbe

r.

24. N

UM

BER

S F

ive

tim

es t

he

sum

of

a n

um

ber

and

3 is

th

e sa

me

as 3

mu

ltip

lied

by

1 le

ss

than

tw

ice

the

nu

mbe

r. W

hat

is

the

nu

mbe

r?

25. N

UM

BER

TH

EORY

Tri

plin

g th

e gr

eate

r of

tw

o co

nse

cuti

ve e

ven

in

tege

rs g

ives

th

e sa

me

resu

lt a

s su

btra

ctin

g 10

fro

m t

he

less

er e

ven

in

tege

r. W

hat

are

th

e in

tege

rs?

26. G

EOM

ETRY

Th

e fo

rmu

la f

or t

he

peri

met

er o

f a

rect

angl

e is

P =

2�, +

2w

, wh

ere

� i

s th

e le

ngt

h a

nd

w i

s th

e w

idth

. A r

ecta

ngl

e h

as a

per

imet

er o

f 24

in

ches

. Fin

d it

s di

men

sion

s if

its

len

gth

is

3 in

ches

gre

ater

th

an i

ts w

idth

.

all n

um

ber

s

2-

4

1 1 −

3

42

no

so

luti

on

1

5 −

6

-4

-2

1

no

so

luti

on

3

6-

8

17

1 2 −

3

-7

-8

-45

18

-8,

-6

4.5

in. b

y 7.

5 in

.

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2612

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-4

Wor

d Pr

oble

m P

ract

ice

So

lvin

g E

qu

ati

on

s w

ith

th

e V

ari

ab

le o

n E

ach

Sid

e

2-4

Cha

pte

r 2

27

Gle

ncoe

Alg

ebra

1

1.O

LYM

PIC

S In

th

e 20

10 W

inte

r O

lym

pic

Gam

es i

n V

anco

uve

r, C

anad

a, t

he

Un

ited

S

tate

s at

hle

tes

won

1 m

ore

than

4 t

imes

th

e n

um

ber

of g

old

met

als

won

by

the

Fre

nch

ath

lete

s. T

he

Un

ited

Sta

tes

won

7

mor

e go

ld m

etal

s th

an t

he

Fre

nch

. S

olve

th

e eq

uat

ion

7 +

F=

4F

+ 1

to

fin

d th

e n

um

ber

of g

old

met

als

won

by

the

Fre

nch

ath

lete

s.

2. A

GE

Die

go’s

mot

her

is

twic

e as

old

as

he

is. S

he

is a

lso

as o

ld a

s th

e su

m o

f th

e ag

es o

f D

iego

an

d bo

th o

f h

is y

oun

ger

twin

bro

ther

s. T

he

twin

s ar

e 11

yea

rs

old.

Sol

ve t

he

equ

atio

n 2

d =

d +

11

+ 1

1 to

fin

d th

e ag

e of

Die

go.

3. G

EOM

ETRY

Su

pple

men

tary

an

gles

ar

e an

gles

wh

ose

mea

sure

s h

ave

a su

m

of 1

80º.

Com

plem

enta

ry a

ngl

es a

re

angl

es w

hos

e m

easu

res

hav

e a

sum

of

90º

. Fin

d th

e m

easu

re o

f an

an

gle

wh

ose

supp

lem

ent

is 1

0º m

ore

than

tw

ice

its

com

plem

ent.

Let

90

– x

equ

al t

he

degr

ee m

easu

re o

f it

s co

mpl

emen

t an

d 18

0 –

x eq

ual

th

e de

gree

mea

sure

of

its

supp

lem

ent.

Wri

te a

nd

solv

e an

equ

atio

n.

4. N

ATU

RE

Th

e ta

ble

show

s th

e cu

rren

t h

eigh

ts a

nd

aver

age

grow

th r

ates

of

two

diff

eren

t sp

ecie

s of

tre

es. H

ow l

ong

wil

l it

tak

e fo

r th

e tw

o tr

ees

to b

e th

e sa

me

hei

ght?

5. N

UM

BER

TH

EORY

Mrs

. Sim

ms

told

h

er c

lass

to

fin

d tw

o co

nse

cuti

ve e

ven

in

tege

rs s

uch

th

at t

wic

e th

e le

sser

of

two

in

tege

rs i

s 4

less

th

an t

wo

tim

es t

he

grea

ter

inte

ger.

a.

Wri

te a

nd

solv

e an

equ

atio

n t

o fi

nd

the

inte

gers

.

b

. Doe

s th

e eq

uat

ion

hav

e on

e so

luti

on,

no

solu

tion

s, o

r is

it

an i

den

tity

? E

xpla

in.

Tree

Sp

ecie

sC

urr

ent

Hei

gh

tA

nn

ual

gro

wth

A38

inch

es4

inch

es

B

45.5

inch

es

2.5

inch

es

2

2

2 ye

ars

old

1

80 -

x =

10

+ 2

(90

- x

); 1

0

3

8 +

4x =

45.

5 +

2.5

x

1.5

x =

7.5

x =

5 y

ears

L

et in

teg

ers

be

n a

nd

(n

+ 2

)

2n =

2(n

+ 2

) -

4

2n

= 2

n +

4 -

4

2n =

2n

1 =

1, n

≠ 0

I

t is

an

iden

tity

bec

ause

it

is t

rue

for

ever

y p

air

of

con

secu

tive

eve

n in

teg

ers.

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2712

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-4

Cha

pte

r 2

28

Gle

ncoe

Alg

ebra

1

Iden

titi

es

An

equ

atio

n t

hat

is

tru

e fo

r ev

ery

valu

e of

th

e va

riab

le i

s ca

lled

an

id

enti

ty.

Wh

en y

ou t

ry t

o so

lve

an i

den

tity

, you

en

d u

p w

ith

a

stat

emen

t th

at i

s al

way

s tr

ue.

Her

e is

an

exa

mpl

e.

S

olve

8 -

(5

- 6

x) =

3(1

+ 2

x).

8 -

(5

- 6

x) =

3(1

+ 2

x)

Ori

gin

al equation

8 -

5 -

(-

6x)

= 3

(1 +

2x)

D

istr

ibutive

Pro

pert

y

8 -

5 +

6x

= 3

+ 6

x

Dis

trib

utive

Pro

pert

y

3

+ 6

x =

3 +

6x

A

dd.

Exer

cise

s S

tate

wh

eth

er e

ach

eq

uat

ion

is

an i

den

tity

. If

it i

s n

ot, f

ind

its

sol

uti

on.

1. 2

(2 -

3x)

= 3

(3 +

x)

+ 4

2.

5(m

+ 1

) +

6 =

3(4

+ m

) +

(2m

- 1

)

3. (

5t +

9) -

(3t

- 1

3) =

2(1

1 +

t)

4. 1

4 -

(6 -

3c)

= 4

c -

c

5. 3

y -

2(y

+ 1

9) =

9y

- 3

(9 -

y)

6. 3

(3h

- 1

) = 4

(h +

3)

7. U

se t

he

tru

e eq

uat

ion

3x

- 2

= 3

x -

2 t

o cr

eate

an

ide

nti

ty o

f yo

ur

own

.

8. U

se t

he

fals

e eq

uat

ion

1 =

2 t

o cr

eate

an

equ

atio

n w

ith

no

solu

tion

.

9. C

reat

e an

equ

atio

n w

hos

e so

luti

on i

s x

= 3

.

Exam

ple

x

= -

1 id

enti

ty

i

den

tity

n

o s

olu

tio

n

y

= -

1 h

= 3

S

amp

le a

nsw

er:

6x -

4 =

2(3

x -

2)

S

amp

le a

nsw

er:

2x +

1 =

2x +

2

S

amp

le a

nsw

er:

4x +

2(x

+ 1

) =

20

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2812

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-4

Gra

phin

g Ca

lcul

ator

Act

ivit

yS

olv

ing

Lin

ear

Eq

uati

on

s

2-4

Cha

pte

r 2

29

Gle

ncoe

Alg

ebra

1

S

olve

5x

- 9

= -

3x +

7.

En

ter

the

left

sid

e of

th

e eq

uat

ion

in

to Y

1 an

d th

e ri

ght

side

in

to t

he

Y2 .

Key

stro

kes:

Y=

5

— 9

EN

TE

R (

–)

3

+

7

Gra

ph t

he

equ

atio

ns.

Key

stro

kes:

Z

OO

M 0

Z

OO

M 8

EN

TE

R

Use

th

e T

RA

CE

key

to

fin

d th

e in

ters

ecti

on.

Not

ice

the

coor

din

ates

at

the

bott

om o

f th

e sc

reen

do

not

ch

ange

as

you

tog

gle

up

and

dow

n. T

his

in

dica

tes

a co

mm

on s

olu

tion

, 2.

Su

bsti

tute

2 i

nto

th

e eq

uat

ion

to

chec

k th

e an

swer

.

Sol

ve 3 −

4 a +

16

= 2

- 1 −

8 a.

En

ter

each

sid

e of

th

e eq

uat

ion

in

to Y

= l

ist.

Key

stro

kes:

Y=

(

3 ÷

4

)

+

16

EN

TE

R 2

—

( 1

÷

8

)

G

RA

PH

.

TR

AC

E t

o lo

cate

th

e po

int

of i

nte

rsec

tion

at

x =

-16

. So,

th

e so

luti

on t

o th

e eq

uat

ion

is

a =

-16

.

On

e w

ay t

o so

lve

a li

nea

r eq

uat

ion

in

on

e va

riab

le i

s to

gra

ph e

ach

sid

e of

th

e eq

uat

ion

as

a se

para

te e

nti

ty. T

he

inte

rsec

tion

of

thes

e tw

o gr

aph

s id

enti

fies

th

e x

valu

e fo

r w

hic

h t

he

equ

atio

n i

s tr

ue.

[-47

, 47]

scl

:10

by [-

31, 3

1] s

cl:1

0

[-47

, 47]

scl

:10

by [-

31, 3

1] s

cl:1

0

Exer

cise

s S

olve

eac

h e

qu

atio

n.

1. 7

(x -

3) =

7

2. 5

- 1

−

2

(x -

6)

= 4

3.

1 −

4 (7

+ 3

z) =

- z −

8

4. 2

8 -

2.2

x =

11.

6x +

262

.6

5. 1

.03x

- 4

= -

2.15

x +

8.7

2 6.

c +

1

−

8

- 2

- c

−

3 =

5 −

6

7. 6

x -

2(x

- 3

) = 4

(x +

1) +

4

8. 5

(x -

2)

+ 2

x =

7(x

+ 4

) -

38

9. 8

−

x =

2x

Not

all

eq

uat

ion

s h

ave

inte

ger

solu

tion

s. I

nve

stig

ate

usi

ng

2nd

[C

AL

C]

5 to

sol

ve t

hes

e eq

uat

ion

s.

10. 2

.4(2

x +

3) =

-0.

1(2x

+ 3

) 11

. 9 -

2(5

d +

4) =

-3(

2d -

7) -

10

Exam

ple

1

Exam

ple

2

4 8

-2

-17

4

3

no

so

luti

on

al

l nu

mb

ers

2, -

2

-1.

5 -

5 −

2

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

2912

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

2-5

Stud

y G

uide

and

Inte

rven

tion

So

lvin

g E

qu

ati

on

s I

nvo

lvin

g A

bso

lute

Valu

e

Cha

pte

r 2

30

Gle

ncoe

Alg

ebra

1

Ab

solu

te V

alu

e Ex

pre

ssio

ns

Exp

ress

ion

s w

ith

abs

olu

te v

alu

es d

efin

e an

upp

er a

nd

low

er r

ange

in

wh

ich

a v

alu

e m

ust

lie

. Exp

ress

ion

s in

volv

ing

abso

lute

val

ue

can

be

eval

uat

ed u

sin

g th

e gi

ven

val

ue

for

the

vari

able

.

E

valu

ate

⎪ t -

5⎪ -

7 i

f t

= 3

.

⎪ t -

5⎪ -

7 =

⎪3

- 5

⎪ -

7

Rep

lace

t w

ith 3

.

=

⎪-

2⎪ -

7

3 -

5 =

-2

=

2 -

7

⎪ -2⎪

= 2

= -

5 S

impl

ify.

Exer

cise

sE

valu

ate

each

exp

ress

ion

if

r =

-2,

n =

-3,

an

d t

= 3

.

1. ⎪

8 -

t⎪ +

3 8

2.

⎪t

- 3

⎪ -

7 -

7 3.

5 +

⎪3

- n

⎪ 1

1

4. ⎪

r +

n⎪ -

7 -

2 5.

⎪n

- t

⎪ +

4 1

0 6.

- ⎪r

+ n

+ t

⎪ -

2

Eva

luat

e ea

ch e

xpre

ssio

n i

f n

= 2

, q =

-

1.5,

r =

-

3, v

= -

8, w

= 4

.5, a

nd

x =

4.

7. ⎪

2q +

r⎪

6 8.

10

- ⎪

2n +

v⎪ 6

9.

⎪3x

- 2

w⎪ -

q 4

.5

10. v

- ⎪

3n +

x⎪ -

18

11. 1

+ ⎪

5q -

w⎪

13

12. 2

⎪3r

- v

⎪ 2

13. ⎪

-2x

+ 5

n⎪ +

(n

- x

) 0

14. 4

w -

⎪2r

+ v

⎪ 4

15

. 3 w

- n

-

5

q -

r

0

Exam

ple

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3012

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-5

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

So

lvin

g E

qu

ati

on

s I

nvo

lvin

g A

bso

lute

Valu

e

2-5

Cha

pte

r 2

31

Gle

ncoe

Alg

ebra

1

Ab

solu

te V

alu

e Eq

uat

ion

s W

hen

sol

vin

g eq

uat

ion

s th

at i

nvo

lve

abso

lute

val

ue,

th

ere

are

two

case

s to

con

side

r.C

ase

1: T

he

valu

e in

side

th

e ab

solu

te v

alu

e sy

mbo

ls i

s po

siti

ve.

Cas

e 2:

Th

e va

lue

insi

de t

he

abso

lute

val

ue

sym

bols

is

neg

ativ

e.

S

olve

⎪x

+ 4

⎪ =

1. T

hen

gr

aph

th

e so

luti

on s

et.

Wri

te ⎪

x +

4⎪ =

1 a

s x

+ 4

= 1

or

x +

4 =

-1.

x +

4 =

1

or

x +

4 =

-1

x +

4 -

4 =

1 -

4

x +

4 -

4 =

-1

- 4

x =

-3

x

= -

5

Th

e so

luti

on s

et i

s {-

5, -

3}.

Th

e gr

aph

is

show

n b

elow

.

-8

-7

-6

-5

-4

-3

-2

-1

0

W

rite

an

eq

uat

ion

in

volv

ing

abso

lute

val

ue

for

the

grap

h.

Fin

d th

e po

int

that

is

the

sam

e di

stan

ce

from

-2

as i

t is

fro

m 4

.

Th

e di

stan

ce f

rom

1 t

o -

2 is

3 u

nit

s. T

he

dist

ance

fro

m 1

to

4 is

3 u

nit

s.S

o, ⎪

x -

1⎪ =

3.

-3

-2

-1

01

23

45

10

-1

-2

-3

23

3 un

its3

units

45

Exer

cise

sS

olve

eac

h e

qu

atio

n. T

hen

gra

ph

th

e so

luti

on s

et.

1. ⎪

y ⎪ =

3 {

-3,

3}

2. ⎪

x -

4⎪ =

4 {

0, 8

} 3.

⎪y

+ 3

⎪ =

2 {

-5,

-1}

-3

-4

-2

-1

01

23

4

0

12

34

56

78

-8

-7

-6

-5

-4

-3

-2

-1

0

4. ⎪

b +

2⎪ =

3 {

-5,

1}

5. ⎪

w -

2⎪ =

5 {

-3,

7}

6. ⎪

t +

2⎪ =

4 {

-6,

2}

-6

-5

-4

-3

-2

-1

01

2

-

8-

6-

4-

20

24

68

-8

-6

-4

-2

02

46

8

7. ⎪

2x⎪ =

8 {

-4,

4}

8. ⎪

5y -

2⎪

= 7

{-

1, 1

4 −

5 }

9. ⎪

p -

0.2

⎪ =

0.5

{-

0.3,

0.7

}

-3

-4

-2

-1

01

23

4

-

3-

4-

2-

10

12

34

-0.

8-

0.4

00.

40.

8

10. ⎪

d -

100

⎪ =

50

{50,

150

} 11

. ⎪2x

- 1

⎪ =

11

{-5,

6}

12. ⎪

3x +

1 −

2 ⎪

= 6

{-

2 1 −

6 , 1

5 −

6 }

5010

015

020

0

-

4-

6-

20

24

68

10

-

2-

3-

10

12

34

5

Wri

te a

n e

qu

atio

n i

nvo

lvin

g ab

solu

te v

alu

e fo

r ea

ch g

rap

h.

13.

0-

2-

4-

6-

82

46

8

14.

-3

-4

-2

-1

01

23

4

15.

-3

-4

-5

-6

-7

-2

-1

01

⎪

x⎪ =

4

⎪x -

1⎪

= 2

⎪

x +

3⎪ =

4

Exam

ple

1Ex

amp

le 2

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3112

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Skill

s Pr

acti

ceS

olv

ing

Eq

uati

on

s I

nvo

lvin

g A

bso

lute

Valu

e

2-5

Cha

pte

r 2

32

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n i

f a

= 2

, b =

-3,

an

d c

= -

4.

1.

⎪ a -

5⎪ -

1 2

2.

⎪b

+ 1

⎪ +

8 1

0

3. 5

- ⎪

c +

1⎪ 2

4.

⎪a

+ b

⎪ -

c 5

Sol

ve e

ach

eq

uat

ion

. Th

en g

rap

h t

he

solu

tion

set

.

5. ⎪

w +

1⎪ =

5 {

-6,

4}

6. ⎪

c -

3⎪ =

1 {

2, 4

}

7. ⎪

n +

2⎪ =

1 {

-3,

-

1}

8. ⎪

t +

6⎪ =

4 {

-10

, -2}

9. ⎪

w -

2⎪ =

2 {

0, 4

} 10

. ⎪k

- 5

⎪ =

4 {

1, 9

}

Wri

te a

n e

qu

atio

n i

nvo

lvin

g ab

solu

te v

alu

e fo

r ea

ch g

rap

h.

11.

-5

-4

-3

-2

-1

01

23

45

12

.

⎪x ⎪ =

1

⎪x +

3⎪ =

2

13.

14.

⎪ x

- 4

⎪ =

1

⎪x ⎪ =

4

-2

-1

-4

-5

-6

-3

01

23

4-

8-

7-

10-

9-

6-

5-

4-

3-

2-

10

01

23

45

67

89

10

-2

-3

-4

-5

-6

-7

-1

01

23

-2

-3

-4

-5

-1

01

23

45

-2

-3

-4

-5

-1

01

23

45

-3

-4

-5

-6

-2

-1

01

23

4-

3-

10

12

34

56

-2

7

-3

-4

-2

-1

01

23

45

6

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3212

/23/

10

2:20

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 2-5

Prac

tice

So

lvin

g E

qu

ati

on

s I

nvo

lvin

g A

bso

lute

Valu

e

2-5

Cha

pte

r 2

33

Gle

ncoe

Alg

ebra

1

Eva

luat

e ea

ch e

xpre

ssio

n i

f x

= -

1, y

= 3

, an

d z

= -

4.

1. 1

6 -

⎪2z

+ 1

⎪ 9

2.

⎪x

- y

⎪ +

4 8

3. ⎪

-3y

+ z

⎪ -

x 1

4 4.

3 ⎪ z

- x

⎪ +

⎪2

- y

⎪ 10

Sol

ve e

ach

eq

uat

ion

. Th

en g

rap

h t

he

solu

tion

set

.

5. |

2z -

9|

= 1

{4,

5}

6. |

3 -

2r|

= 7

{-

2, 5

}

-

5-

4-

3-

2-

10

12

34

5

-

5-

4-

3-

2-

10

12

34

5

7. |

3t +

6|

= 9

{-

5, 1

} 8.

|2 g

- 5

| =

9 {

-2,

7}

-5

-4

-3

-2

-1

01

23

45

-2

-1

01

23

45

67

8

Wri

te a

n e

qu

atio

n i

nvo

lvin

g ab

solu

te v

alu

e fo

r ea

ch g

rap

h.

9.

12

34

56

78

910

11

10.

-2

-3

-4

-5

-6

-7

-8

-1

01

2

⎪

x -

6⎪ =

5

⎪ x

+ 4

⎪ =

2

11.

-2

-3

-4

-5

-6

-7

-8

-1

01

2

12.

-2

-3

-1

01

23

45

67

⎪

x +

3⎪ =

4

⎪ x

- 2

⎪ =

4

13. F

ITN

ESS

Tai

sha

use

s th

e el

lipt

ical

cro

ss-t

rain

er a

t th

e gy

m. H

er g

ener

al g

oal

is t

o bu

rn

280

Cal

orie

s pe

r w

orko

ut,

bu

t sh

e va

ries

by

as m

uch

as

25 C

alor

ies

from

th

is a

mou

nt

on

any

give

n d

ay. W

rite

an

d so

lve

an e

quat

ion

to

fin

d th

e m

axim

um

an

d m

inim

um

nu

mbe

r of

Cal

orie

s T

aish

a bu

rns

on t

he

cros

s-tr

ain

er.

{

⎪ c -

280

⎪

= 2

5; m

in =

255

; m

ax =

305

}

14. T

EMPE

RA

TUR

E A

th

erm

omet

er i

s gu

aran

teed

to

give

a t

empe

ratu

re n

o m

ore

than

1.

2°F

fro

m t

he

actu

al t

empe

ratu

re. I

f th

e th

erm

omet

er r

eads

28°

F, w

rite

an

d so

lve

an

equ

atio

n t

o fi

nd

the

max

imu

m a

nd

min

imu

m t

empe

ratu

res

it c

ould

be.

{

⎪ t -

28⎪

= 1.

2; m

in =

26.

8°F

; m

ax =

29.

2°F

}

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3312

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

So

lvin

g O

pen

Sen

ten

ces I

nvo

lvin

g A

bso

lute

Valu

e

2-5

Cha

pte

r 2

34

Gle

ncoe

Alg

ebra

1

1.EN

GIN

EER

ING

Tol

eran

ce i

n e

ngi

nee

rin

g is

an

all

owan

ce m

ade

for

impe

rfec

tion

s in

a

man

ufa

ctu

red

obje

ct. T

he

man

ufa

ctu

rer

of a

n o

ven

spe

cifi

es a

tem

pera

ture

to

lera

nce

of ±

15ºF

. Th

is m

ean

s th

at t

he

tem

pera

ture

in

side

th

e ov

en w

ill

be

wit

hin

15º

F o

f th

e te

mpe

ratu

re t

hat

it

is s

et o

n. W

rite

an

abs

olu

te v

alu

e ex

pres

sion

to

repr

esen

t th

e m

axim

um

an

d m

inim

um

tem

pera

ture

s in

side

th

e ov

en w

hen

th

e th

erm

osta

t is

set

on

400

ºF.

⎪t

- 4

00⎪

= 1

5

2. A

VIA

TIO

N T

he

circ

le g

raph

sh

ows

the

resu

lts

of a

su

rvey

th

at a

sked

430

0 st

ude

nts

age

s 7

to 1

8 w

hat

th

ey t

hou

ght

wou

ld b

e th

e m

ost

impo

rtan

t be

nef

it o

f ai

r tr

avel

in

th

e fu

ture

. Th

ere

are

abou

t 40

mil

lion

stu

den

ts i

n t

he

Un

ited

Sta

tes.

If

th

e m

argi

n o

f er

ror

is ±

3%, w

hat

is

the

ran

ge o

f th

e n

um

ber

of s

tude

nts

age

s 7

to

18 w

ho

wou

ld l

ikel

y sa

y th

at “

fin

din

g n

ew r

esou

rces

for

Ear

th”

is t

he

mos

t im

port

ant

ben

efit

of

futu

re f

ligh

t?

So

urce

:Th

e W

orld

Alm

anac

3.C

OLL

EGE

A c

erta

in s

chol

arsh

ip a

nd

stu

den

t lo

an f

un

d u

ses

a fo

rmu

la t

o de

term

ine

wh

eth

er o

r n

ot a

stu

den

t qu

alif

ies

for

coll

ege

fun

din

g. T

he

form

ula

is

⎪3k

+ 6

⎪ =

15,

wh

ere

k is

a n

eed

scor

e de

term

ined

by

an i

nte

rvie

w. W

hat

are

th

e po

ssib

le n

eed

scor

es?

{

-7,

3}

4. S

TATI

STIC

S T

he

mos

t fa

mil

iar

stat

isti

cal

mea

sure

is

the

arit

hm

etic

m

ean

, or

aver

age.

A s

econ

d im

port

ant

stat

isti

cal

mea

sure

is

the

stan

dard

de

viat

ion

, wh

ich

is

a m

easu

re o

f h

ow f

ar

the

indi

vidu

al s

core

s ar

e fr

om t

he

mea

n.

For

exa

mpl

e, t

he

mea

n s

core

on

th

e W

ech

sler

IQ

tes

t is

100

an

d th

e st

anda

rd

devi

atio

n i

s 15

. Th

is m

ean

s th

at p

eopl

e w

ith

in o

ne

devi

atio

n o

f th

e m

ean

hav

e IQ

sc

ores

th

at a

re 1

5 po

ints

hig

her

or

low

er

than

th

e m

ean

.

a. W

rite

an

abs

olu

te v

alu

e eq

uat

ion

to

fin

d th

e m

axim

um

an

d m

inim

um

tes

t sc

ores

wit

hin

on

e st

anda

rd d

evia

tion

if

th

e m

ean

was

80

and

the

stan

dard

de

viat

ion

was

12.

⎪ t

- 8

0⎪ =

12

b.

Wh

at i

s th

e ra

nge

of W

ech

sler

IQ

tes

t sc

ores

±3

stan

dard

dev

iati

ons

from

th

e m

ean

?

55 t

o 1

45

43%

26%

10%21

%

Find

ing

new

res

ourc

esfo

r E

arth

The

Nex

t Fr

ont

ier

for

Flig

ht

Sci

entifi

cex

per

imen

tsin

sp

ace

Flyi

ng fa

ster

from

one

cont

inen

tto

ano

ther

Exp

lorin

g ot

her

pla

nets

in o

ur s

olar

sys

tem

for

sign

s of

life

bet

wee

n 7

,20

0,0

00

and

9,6

00,

00

0

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3412

/23/

10

12:0

0 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-5

Enri

chm

ent

2-5

Cha

pte

r 2

35

Gle

ncoe

Alg

ebra

1

Pre

cis

ion

of

Measu

rem

en

tT

he

prec

isio

n o

f a

mea

sure

men

t de

pen

ds b

oth

on

you

r ac

cura

cy i

n

mea

suri

ng

and

the

nu

mbe

r of

div

isio

ns

on t

he

rule

r yo

u u

se. S

upp

ose

you

mea

sure

d a

len

gth

of

woo

d to

th

e n

eare

st o

ne-

eigh

th o

f an

in

ch

and

got

a le

ngt

h o

f 6

5 −

8 i

n.

Th

e dr

awin

g sh

ows

that

th

e ac

tual

mea

sure

men

t li

es s

omew

her

e

betw

een

6 9 − 16

in

. an

d 6

11 − 16 i

n. T

his

mea

sure

men

t ca

n b

e w

ritt

en u

sin

g

th

e sy

mbo

l ±

, wh

ich

is

read

plu

s or

min

us.

6 5 − 8

±1 − 16

in

.

In t

his

exa

mpl

e,

1 − 16 i

n. i

s th

e ab

solu

te e

rror

. Th

e ab

solu

te e

rror

is

one-

hal

f th

e sm

alle

st u

nit

use

d in

a m

easu

rem

ent.

Fin

d t

he

max

imu

m a

nd

min

imu

m l

engt

hs

for

each

mea

sure

men

t.

1. 3

1 −

2 ±

1 −

4 i

n.

2. 9

.78

± 0

.005

cm

3.

2.4

± 0

.05

g

3

1 −

4 in

.; 3

3 −

4 in

. 9

.775

cm

; 9.

785

cm

2.3

5 g

; 2.

45 g

4. 2

8 ±

1 −

2 f

t 5.

15

± 0

.5 c

m

6. 11

−

16

±

1 −

64 i

n.

2

7 1 −

2 ft;

28

1 −

2 ft

14.

5 cm

; 15

.5 c

m

43

−

64 i

n.;

45

−

64 i

n.

For

eac

h m

easu

rem

ent,

giv

e th

e sm

alle

st u

nit

use

d a

nd

th

e ab

solu

te e

rror

.

7. T

he

actu

al m

easu

rem

ent

is b

etw

een

12.

5 cm

an

d 13

.5 c

m.

1 cm

; ±

0.5

cm

8. T

he

actu

al m

easu

rem

ent

is b

etw

een

12

1 −

8 i

n. a

nd

12 3 −

8 i

n.

1 −

4 in

.; ±

1 −

8 in

.

9. T

he

actu

al m

easu

rem

ent

is b

etw

een

56

1 −

2 i

n. a

nd

57 1 −

2 i

n.

1 in

.; ±

1 −

2 in

.

10. T

he

actu

al m

easu

rem

ent

is b

etw

een

23.

05 m

m a

nd

23.1

5 m

m.

0.1

mm

; ±

0.0

5 m

m

56

78

6 5 – 8

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3512

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

Rati

os a

nd

Pro

po

rtio

ns

2-6

Cha

pte

r 2

36

Gle

ncoe

Alg

ebra

1

Rat

ios

and

Pro

po

rtio

ns

A r

atio

is

a co

mpa

riso

n of

tw

o nu

mbe

rs b

y di

visi

on. T

he r

atio

of

x t

o y

can

be

expr

esse

d as

x t

o y,

x:y

or

x −

y . R

atio

s ar

e u

sual

ly e

xpre

ssed

in

sim

ples

t fo

rm.

An

equ

atio

n s

tati

ng

that

tw

o ra

tios

are

equ

al i

s ca

lled

a p

rop

orti

on. T

o de

term

ine

wh

eth

er

two

rati

os f

orm

a p

ropo

rtio

n, e

xpre

ss b

oth

rat

ios

in s

impl

est

form

or

chec

k cr

oss

prod

uct

s.

D

eter

min

e w

het

her

th

e

rati

os 24

−

36 a

nd

12

−

18 a

re e

qu

ival

ent

rati

os.

Wri

te y

es o

r n

o. J

ust

ify

you

r an

swer

.

24

−

36 =

2 −

3 w

hen

exp

ress

ed i

n s

impl

est

form

.

12

−

18 =

2 −

3 w

hen

exp

ress

ed i

n s

impl

est

form

.

Th

e ra

tios

24

−

36 a

nd

12

−

18 f

orm

a p

ropo

rtio

n

beca

use

th

ey a

re e

qual

wh

en e

xpre

ssed

in

si

mpl

est

form

.

U

se c

ross

pro

du

cts

to

det

erm

ine

wh

eth

er 10

−

18 a

nd

25

−

45 f

orm

a

pro

por

tion

.

10

−

18 �

25

−

45

Writ

e th

e pr

opor

tion.

10(4

5) �

18(

25)

Cro

ss p

rodu

cts

45

0 =

450

S

impl

ify.

Th

e cr

oss

prod

uct

s ar

e eq

ual

, so

10

−

18 =

25

−

45 .

Sin

ce t

he

rati

os a

re e

qual

, th

ey f

orm

a

prop

orti

on.

Exer

cise

s

Det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

are

equ

ival

ent

rati

os. W

rite

yes

or

no.

1.

1 −

2 ,

16

−

32

2. 5

−

8 , 10

−

15

3.

10

−

20

, 25

−

49

4.

25

−

36 ,

15

−

20

5. 12

−

32

, 3 −

16

6.

4 −

9 ,

12

−

27

7.

0.1

−

2 ,

5 −

10

0 8.

15

−

20 ,

9 −

12

9.

14

−

12

, 20

−

30

10.

2 −

3 ,

20

−

30

11.

5 −

9 ,

25

−

45

12.

72

−

64 ,

9 −

8

13.

5 −

5 ,

30

−

20

14.

18

−

24 ,

50

−

75

15.

100

−

75 ,

44

−

33

16.

0.05

−

1 ,

1 −

20

17.

1.5

−

2 , 6 −

8

18.

0.1

−

0.2 ,

0.45

−

0.9

Exam

ple

1Ex

amp

le 2

y

es

no

n

o

n

o

no

y

es

y

es

yes

n

o

y

es

yes

y

es

n

o

no

y

es

y

es

yes

y

es

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3612

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-6

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Rati

os a

nd

Pro

po

rtio

ns

2-6

Cha

pte

r 2

37

Gle

ncoe

Alg

ebra

1

Solv

e Pr

op

ort

ion

s If

a p

ropo

rtio

n in

volv

es a

var

iabl

e, y

ou c

an u

se c

ross

pro

duct

s to

sol

veth

e pr

opor

tion

. In

th

e pr

opor

tion

x −

5 =

10

−

13 ,

x an

d 13

are

cal

led

extr

emes

. Th

ey a

re t

he

firs

t

and

last

ter

ms

of t

he

prop

orti

on. 5

an

d 10

are

cal

led

mea

ns.

The

y ar

e th

e m

iddl

e te

rms

of t

he

prop

orti

on. I

n a

prop

orti

on, t

he p

rodu

ct o

f the

ext

rem

es is

equ

al t

o th

e pr

oduc

t of

the

mea

ns.

S

olve

x −

5 = 10

−

13 .

x −

5 =

10

−

13

Orig

inal

pro

port

ion

13(

x) =

5(1

0)

Cro

ss p

rodu

cts

13

x =

50

Sim

plify

.

13x

−

13

= 50

−

13

Di

vide

eac

h si

de b

y 13

.

x

= 3

11

−

13

Sim

plify

.

Exer

cise

sS

olve

eac

h p

rop

orti

on. I

f n

eces

sary

, rou

nd

to

the

nea

rest

hu

nd

red

th.

1.

-3

−

x =

2 −

8

2.

1 −

t = 5 −

3

3.

0.1

−

2 =

0.5

−

x

4.

x +

1

−

4

= 3 −

4

5.

4 −

6 =

8 −

x

6.

x −

21

=

3 −

63

7.

9 −

y

+ 1

= 18

−

54

8.

3 −

d =

18

−

3

9.

5 −

8 =

p

−

24

10.

4 −

b

- 2

=

4 −

12

11

. 1.

5 −

x

= 12

−

x

12

. 3

+ y

−

4

= -

y −

8

13.

a -

18

−

12

=

15

−

3

14.

12

−

k =

24

−

k

15.

2 +

w

−

6 =

12

−

9

Use

a p

rop

orti

on t

o so

lve

each

pro

ble

m.

16. M

OD

ELS

To

mak

e a

mod

el o

f th

e G

uad

elou

pe R

iver

bed

, Her

mie

use

d 1

inch

of

clay

for

5

mil

es o

f th

e ri

ver’

s ac

tual

len

gth

. His

mod

el r

iver

was

50

inch

es l

ong.

How

lon

g is

th

e G

uad

elou

pe R

iver

?

17. E

DU

CA

TIO

N J

osh

fin

ish

ed 2

4 m

ath

pro

blem

s in

on

e h

our.

At

that

rat

e, h

ow m

any

hou

rs w

ill

it t

ake

him

to

com

plet

e 72

pro

blem

s?

Mea

ns-

Ext

rem

es P

rop

erty

of

Pro

po

rtio

ns

For

any

num

bers

a, b

, c, a

nd d

, if

a −

b =

c −

d ,

then

ad

= b

c.

Exam

ple

-12

10

212

1

2615

14n

o s

olu

tio

n-

2

78n

o s

olu

tio

n6

250

mi

3 h

1 −

2

3 −

5

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3712

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Skill

s Pr

acti

ceR

ati

os a

nd

Pro

po

rtio

ns

2-6

Cha

pte

r 2

38

Gle

ncoe

Alg

ebra

1

Det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

are

equ

ival

ent

rati

os. W

rite

yes

or

no.

1.

4 −

5 ,

20

−

25

2.

5 −

9 ,

7 −

11

3.

6 −

7 ,

24

−

28

4. 8 −

9 ,

72

−

81

5.

7 −

16 ,

42

−

90

6. 13

−

19

, 26

−

38

7.

3 −

14 ,

21

−

98

8. 12

−

17

, 50

−

85

Sol

ve e

ach

pro

por

tion

. If

nec

essa

ry, r

oun

d t

o th

e n

eare

st h

un

dre

dth

.

9.

1 −

a

=

2 −

14

10.

5 −

b =

3 −

9

11.

9

−

g =

15

−

10

12.

3 −

a

= 1 −

6

13.

6

−

z =

3 −

5

14.

5 −

f = 35

−

21

15.

12

−

7 =

36

−

m

16

. 6 −

23

=

y −

69

17.

42

−

56 =

6 −

f

18.

7 −

b =

1 −

9

19.

10

−

14 =

30

−

m

20

. 11

−

15

=

n

−

60

21.

9 −

c =

27

−

39

22.

5 −

12 =

20

−

g

23.

4 −

21 =

y −

84

24

. 22

−

x

= 11

−

30

25. B

OA

TIN

G H

ue’

s bo

at u

sed

5 ga

llon

s of

gas

olin

e in

4 h

ours

. At

this

rat

e,h

ow m

any

gall

ons

of g

asol

ine

wil

l th

e bo

at u

se i

n 1

0 h

ours

?

yes

no

yes

yes

no

yes

yes

no

715

618

103

2118

863

4244

1348

1660

12.5

gal

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3812

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-6

Prac

tice

Rati

os a

nd

Pro

po

rtio

ns

2-6

Cha

pte

r 2

39

Gle

ncoe

Alg

ebra

1

Det

erm

ine

wh

eth

er e

ach

pai

r of

rat

ios

are

equ

ival

ent

rati

os. W

rite

yes

or

no.

1.

7 −

6 ,

52

−

48

2.

3 −

11

, 15

−

66

3. 18

−

24

, 36

−

48

4.

12

−

11 ,

108

−

99

5.

8 −

9 ,

72

−

81

6.

1.5

−

9 , 1 −

6

7.

3.4

−

5.2 ,

7.14

−

10.9

2

8.

1.7

−

1.2 ,

2.9

−

2.4

9.

7.6

−

1.8 ,

3.9

−

0.9

Sol

ve e

ach

pro

por

tion

. If

nec

essa

ry, r

oun

d t

o th

e n

eare

st h

un

dre

dth

.

10.

5 −

a

= 30

−

54

11

. v −

46

= 34

−

23

12

. 40

−

56

= k −

7

13. 28

−

49

= 4 −

w

14

. 3 −

u =

27

−

162

15.

y −

3 =

48

−

9

16. 2

−

y =

10

−

60

17.

5 −

11

= 35

−

x

18

. 3 −

51

=

z −

17

19.

6 −

61

= 12

−

h

20

. g −

16

= 6 −

4

21.

14

−

49 =

2 −

a

22. 7

−

9 = 8 −

t

23.

3 −

q

= 5 −

6

24.

m

−

6 = 5 −

8

25.

v −

0.

23 =

7

−

1.61

26

. 3

−

0.72

= 12

−

b

27

. 6 −

n =

3

−

0.51

28.

7 −

a

- 4

= 14

−

6

29

. 3 −

12

=

2 −

y

+ 6

30

. m

- 1

−

8 =

2 −

4

31.

5 −

12

= x

+ 1

−

4

32. r

+ 2

−

7 =

5 −

7

33.

3 −

7 =

x -

2

−

6

34. P

AIN

TIN

G Y

sidr

a pa

ints

a r

oom

th

at h

as 4

00 s

quar

e fe

et o

f w

all

spac

e in

2 1 −

2 h

ours

.

A

t th

is r

ate,

how

lon

g w

ill

it t

ake

her

to

pain

t a

room

th

at h

as 7

20 s

quar

e fe

et o

f w

all

spac

e?

35. V

AC

ATI

ON

PLA

NS

Wal

ker

is p

lan

nin

g a

sum

mer

vac

atio

n. H

e w

ants

to

visi

t P

etri

fied

N

atio

nal

For

est

and

Met

eor

Cra

ter,

Ari

zon

a, t

he

50,0

00-y

ear-

old

impa

ct s

ite

of a

lar

ge

met

eor.

On

a m

ap w

ith

a s

cale

wh

ere

2 in

ches

equ

als

75 m

iles

, th

e tw

o ar

eas

are

abou

t

1 1 −

2 i

nch

es a

part

. Wh

at i

s th

e di

stan

ce b

etw

een

Pet

rifi

ed N

atio

nal

For

est

and

Met

eor

Cra

ter?

no

no

yes

yes

yes

yes

yes

no

no

968

5

718

16

1277

1

122

247

10 2 −

7 3

3 −

5

3 3 −

4

12.

881.

02

72

5

2 −

3 3

4 4 −

7

4 1 −

2 h

abo

ut

56.2

5 m

i

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

3912

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

Rati

os a

nd

Pro

po

rtio

ns

2-6

Cha

pte

r 2

40

Gle

ncoe

Alg

ebra

1

1. W

ATE

R A

dri

ppin

g fa

uce

t w

aste

s 3

cups

of

wat

er e

very

24

hou

rs. H

ow m

uch

w

ater

is

was

ted

in a

wee

k?

2. G

ASO

LIN

E In

Nov

embe

r 20

10 t

he

aver

age

pric

e of

5 g

allo

ns

of r

egu

lar

un

lead

ed g

asol

ine

in t

he

Un

ited

Sta

tes

was

$14

.46.

Wh

at w

as t

he

pric

e fo

r 16

gal

lon

s of

gas

?

3. S

HO

PPIN

G S

teve

nso

n’s

Mar

ket

is

sell

ing

3 pa

cks

of t

ooth

pick

s fo

r $0

.87.

H

ow m

uch

wil

l 10

pac

ks o

f to

oth

pick

s co

st a

t th

is p

rice

? R

oun

d yo

ur

answ

er t

o th

e n

eare

st c

ent.

4. B

UIL

DIN

GS

Wil

lis

Tow

er i

n C

hic

ago

is

1450

fee

t ta

ll. T

he

Joh

n H

anco

ck C

ente

r in

Ch

icag

o is

112

7 fe

et t

all.

Su

ppos

e yo

u

are

aske

d to

bu

ild

a sm

all-

scal

e re

plic

a of

ea

ch. I

f yo

u m

ake

the

Wil

lis

Tow

er

3 m

eter

s ta

ll, w

hat

wou

ld b

e th

e ap

prox

imat

e h

eigh

t of

th

e Jo

hn

Han

cock

re

plic

a? R

oun

d yo

ur

answ

er t

o th

e n

eare

st h

un

dred

th.

5. M

APS

A m

ap o

f Wac

o, T

exas

an

d n

eigh

bori

ng

tow

ns

is s

how

n b

elow

.

a. U

se a

met

ric

rule

r to

mea

sure

th

e di

stan

ces

betw

een

Rob

inso

n a

nd

Nea

le o

n t

he

map

.

b.

Usi

ng

the

scal

e of

th

e m

ap, f

ind

the

appr

oxim

ate

actu

al d

ista

nce

by

air

(not

by

road

s), b

etw

een

Rob

inso

n

and

Nea

le.

c. A

ppro

xim

atel

y h

ow m

any

squ

are

mil

es a

re s

how

n o

n t

his

map

?

05

mi

6

484

84

35

Te

xa

sR

oss

Waco

Neale

Ro

bin

son

Bell

mead

Hew

itt

Ch

ina S

pri

ng

2

1 cu

ps

$

46.2

7

$

2.90

2

.33

met

ers

2 cm

6

.67

mile

s

2

3.3

× 2

3.3

= 5

43 s

qu

are

mile

s

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4012

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-6

Enri

chm

ent

2-6

Cha

pte

r 2

41

Gle

ncoe

Alg

ebra

1

An

gle

s o

f a

Tria

ng

leIn

geo

met

ry, m

any

stat

emen

ts a

bou

t ph

ysic

al s

pace

are

pro

ven

to

be t

rue.

Su

ch s

tate

men

ts

are

call

ed t

heo

rem

s. H

ere

are

two

exam

ples

of

geom

etri

c th

eore

ms.

a.

Th

e su

m o

f th

e m

easu

res

of t

he

angl

es o

f a

tria

ngl

e is

180

°.

b.

If t

wo

side

s of

a t

rian

gle

hav

e eq

ual

mea

sure

, th

en t

he

two

angl

es o

ppos

ite

thos

e si

des

also

hav

e eq

ual

mea

sure

.

For

eac

h o

f th

e tr

ian

gles

, wri

te a

n e

qu

atio

n a

nd

th

en s

olve

for

x. (

A t

ick

mar

k o

n

two

or m

ore

sid

es o

f a

tria

ngl

e in

dic

ates

th

at t

he

sid

es h

ave

equ

al m

easu

re.)

1.

70°

50°

x°

2.

90°

45°

x°

3.

90°

x

4.

(x

+ 3

0)°

x°(5

x +

10)

°

5.

5x°

2x°

x

6.

90°

4x°

5x°

7.

(x -

15)

°

3x°

(x +

30)

°

8.

40°

x°

9.

x°

10

.

x°2x

°

30°

11. T

wo

angl

es o

f a t

rian

gle

have

the

sam

e 12

. The

mea

sure

of o

ne a

ngle

of a

tri

angl

e is

m

easu

re. T

he s

um o

f the

mea

sure

s of

t

wic

e th

e m

easu

re o

f a s

econ

d an

gle.

The

th

ese

angl

es is

one

-hal

f the

mea

sure

of

mea

sure

of t

he t

hird

ang

le is

12

less

tha

n

the

thir

d an

gle.

Fin

d th

e m

easu

res

of

the

sum

of t

he o

ther

tw

o. F

ind

the

the

angl

es o

f the

tri

angl

e.

mea

sure

s of

the

ang

les

of t

he t

rian

gle.

70

+ 5

0 +

x =

180

; x

= 6

0°

30°,

30°

, 120

°64

°, 3

2°, 8

4°

x +

45

+ 9

0 =

180

; x =

45°

x +

x +

90

= 1

80;

x =

45°

(x +

30)

+ x

+

(5x +

10)

= 1

80;

x =

20°

2x +

5x +

x =

180

; x =

22.

5°

4x +

5x +

90

= 1

80;

x =

10°

3x +

(x -

15)

+ (

x +

30)

= 1

80;

x =

33°

40

+ 4

0 +

x =

180

; x =

10

0°

x +

x +

x =

180

; x =

60°

30

+ 2

x +

x =

180

; x =

50°

023_

041_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4112

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

Perc

en

t o

f C

han

ge

2-7

Cha

pte

r 2

42

Gle

ncoe

Alg

ebra

1

Perc

ent

of

Ch

ang

e W

hen

an

in

crea

se o

r de

crea

se i

n a

n a

mou

nt

is e

xpre

ssed

as

a pe

rcen

t, t

he

perc

ent

is c

alle

d th

e p

erce

nt

of c

han

ge. I

f th

e n

ew n

um

ber

is g

reat

er t

han

th

e or

igin

al n

um

ber,

the

perc

ent

of c

han

ge i

s a

per

cen

t of

in

crea

se. I

f th

e n

ew n

um

ber

is

less

th

an t

he

orig

inal

nu

mbe

r, th

e pe

rcen

t of

ch

ange

is

the

per

cen

t of

dec

reas

e.

F

ind

th

e p

erce

nt

of i

ncr

ease

.

ori

gin

al: 4

8n

ew: 6

0F

irst

, su

btra

ct t

o fi

nd

the

amou

nt

of

incr

ease

. Th

e am

oun

t of

in

crea

se i

s 60

- 4

8 =

12.

Th

en f

ind

the

perc

ent

of i

ncr

ease

by

usi

ng

the

orig

inal

nu

mbe

r, 48

, as

the

base

.

12

−

48

=

r −

10

0 P

erce

nt p

ropo

rtio

n

12(

100)

= 4

8(r)

C

ross

pro

duct

s

12

00 =

48r

S

impl

ify.

1200

−

48

= 48

r −

48

D

ivid

e ea

ch s

ide

by 4

8.

25

= r

S

impl

ify.

Th

e pe

rcen

t of

in

crea

se i

s 25

%.

F

ind

th

e p

erce

nt

of d

ecre

ase.

o

rigi

nal

: 30

new

: 22

Fir

st, s

ubt

ract

to

fin

d th

e am

oun

t of

de

crea

se. T

he

amou

nt

of d

ecre

ase

is

30 -

22

= 8

.T

hen

fin

d th

e pe

rcen

t of

dec

reas

e by

usi

ng

the

orig

inal

nu

mbe

r, 30

, as

the

base

.

8 −

30

=

r −

10

0 P

erce

nt p

ropo

rtio

n

8(10

0) =

30(

r)

Cro

ss p

rodu

cts

80

0 =

30r

S

impl

ify.

800

−

30

= 30

r −

30

D

ivid

e ea

ch s

ide

by 3

0.

26 2 −

3 =

r

Sim

plify

.

Th

e pe

rcen

t of

dec

reas

e is

26

2 −

3 %

, or

abou

t 27

%.

Exer

cise

sS

tate

wh

eth

er e

ach

per

cen

t of

ch

ange

is

a p

erce

nt

of i

ncr

ease

or

a p

erce

nt

of

dec

rea

se. T

hen

fin

d e

ach

per

cen

t of

ch

ange

. Rou

nd

to

the

nea

rest

wh

ole

per

cen

t.

1. o

rigi

nal

: 50

2. o

rigi

nal

: 90

3. o

rigi

nal

: 45

new

: 80

new

: 100

n

ew: 2

0

4. o

rigi

nal

: 77.

5 5.

ori

gin

al: 1

40

6. o

rigi

nal

: 135

new

: 62

new

: 150

n

ew: 9

0

7. o

rigi

nal

: 120

8.

ori

gin

al: 9

0 9.

ori

gin

al: 2

7.5

new

: 180

n

ew: 2

70

new

: 25

10. o

rigi

nal

: 84

11. o

rigi

nal

: 12.

5 12

. ori

gin

al: 2

50n

ew: 9

8 n

ew: 1

0 n

ew: 5

00

Exam

ple

2Ex

amp

le 1

i

ncr

ease

; 60

%

in

crea

se;

11%

d

ecre

ase;

56%

d

ecre

ase;

20%

i

ncr

ease

; 7%

d

ecre

ase;

33%

i

ncr

ease

; 50

%

in

crea

se;

200%

d

ecre

ase;

9%

i

ncr

ease

; 17

%

dec

reas

e; 2

0%

in

crea

se;

100%

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4212

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-7

2-7

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Perc

en

t o

f C

han

ge

Cha

pte

r 2

43

Gle

ncoe

Alg

ebra

1

Solv

e Pr

ob

lem

s D

isco

un

ted

pric

es a

nd

pric

es i

ncl

udi

ng

tax

are

appl

icat

ion

s of

per

cen

t of

ch

ange

. Dis

cou

nt

is t

he

amou

nt

by w

hic

h t

he

regu

lar

pric

e of

an

ite

m i

s re

duce

d. T

hu

s,

the

disc

oun

ted

pric

e is

an

exa

mpl

e of

per

cen

t of

dec

reas

e. S

ales

tax

is

an a

mou

nt

that

is

adde

d to

th

e co

st o

f an

ite

m, s

o th

e pr

ice

incl

udi

ng

tax

is a

n e

xam

ple

of p

erce

nt

of i

ncr

ease

.

SA

LES

A c

oat

is o

n s

ale

for

25%

off

th

e or

igin

al p

rice

. If

the

orig

inal

p

rice

of

the

coat

is

$75,

wh

at i

s th

e d

isco

un

ted

pri

ce?

Th

e di

scou

nt

is 2

5% o

f th

e or

igin

al p

rice

.

25%

of

$75

= 0

.25

× 7

5 25

% =

0.2

5

= 1

8.75

U

se a

cal

cula

tor.

Su

btra

ct $

18.7

5 fr

om t

he

orig

inal

pri

ce.

$75

- $

18.7

5 =

$56

.25

Th

e di

scou

nte

d pr

ice

of t

he

coat

is

$56.

25.

Exer

cise

s F

ind

th

e to

tal

pri

ce o

f ea

ch i

tem

.

1. S

hir

t: $

24.0

0 2.

CD

pla

yer:

$14

2.00

3.

Cel

ebri

ty c

alen

dar:

$10

.95

Sal

es t

ax: 4

%

Sal

es t

ax: 5

.5%

S

ales

tax

: 7.5

%

Fin

d t

he

dis

cou

nte

d p

rice

of

each

ite

m.

4. C

ompa

ct d

isc:

$16

5.

Tw

o co

nce

rt t

icke

ts: $

28

6. A

irli

ne

tick

et: $

248.

00D

isco

un

t: 1

5%

Stu

den

t di

scou

nt:

28%

S

upe

rair

dis

cou

nt:

33%

7. V

IDEO

S T

he

orig

inal

sel

lin

g pr

ice

of a

new

spo

rts

vide

o w

as $

65.0

0. D

ue

to t

he

dem

and

the

pric

e w

as i

ncr

ease

d to

$87

.75.

Wh

at w

as t

he

perc

ent

of i

ncr

ease

ove

r th

e or

igin

al

pric

e?

8. S

CH

OO

L A

hig

h s

choo

l pa

per

incr

ease

d it

s sa

les

by 7

5% w

hen

it

ran

an

iss

ue

feat

uri

ng

a co

nte

st t

o w

in a

cla

ss p

arty

. Bef

ore

the

con

test

iss

ue,

10%

of

the

sch

ool’s

800

stu

den

ts

bou

ght

the

pape

r. H

ow m

any

stu

den

ts b

ough

t th

e co

nte

st i

ssu

e?

9. B

ASE

BA

LL B

aseb

all

tick

ets

cost

$15

for

gen

eral

adm

issi

on o

r $2

0 fo

r bo

x se

ats.

Th

e sa

les

tax

on e

ach

tic

ket

is 8

%. W

hat

is

the

fin

al c

ost

of e

ach

typ

e of

tic

ket?

Exam

ple

$

13.6

0 $

20.1

6 $

166.

16

$

24.9

6 $

149.

81

$11

.77

35%

140

stu

den

ts

$16.

20;

$21.

60

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4312

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Skill

s Pr

acti

ceP

erc

en

t o

f C

han

ge

2-7

Cha

pte

r 2

44

Gle

ncoe

Alg

ebra

1

Sta

te w

het

her

eac

h p

erce

nt

of c

han

ge i

s a

per

cen

t of

in

crea

se o

r a

per

cen

t of

d

ecre

ase

. Th

en f

ind

eac

h p

erce

nt

of c

han

ge. R

oun

d t

o th

e n

eare

st w

hol

e p

erce

nt.

1. o

rigi

nal

: 25

2. o

rigi

nal

: 50

new

: 10

new

: 75

3. o

rigi

nal

: 55

4. o

rigi

nal

: 25

new

: 50

new

: 28

5. o

rigi

nal

: 50

6. o

rigi

nal

: 90

new

: 30

new

: 95

7. o

rigi

nal

: 48

8. o

rigi

nal

: 60

new

: 60

new

: 45

Fin

d t

he

tota

l p

rice

of

each

ite

m.

9. d

ress

: $69

.00

10. b

inde

r: $

14.5

0ta

x: 5

%

tax

: 7%

11. h

ardc

over

boo

k: $

28.9

5 12

. gro

ceri

es: $

47.5

2ta

x: 6

%

tax

: 3%

13. f

ille

r pa

per:

$6.

00

14. s

hoe

s: $

65.0

0ta

x: 6

.5%

t

ax: 4

%

15. b

aske

tbal

l: $1

7.00

16

. con

cert

tic

kets

: $48

.00

tax:

6%

t

ax: 7

.5%

Fin

d t

he

dis

cou

nte

d p

rice

of

each

ite

m.

17. b

ackp

ack:

$56

.25

18. m

onit

or: $

150.

00di

scou

nt:

20%

d

isco

un

t: 5

0%

19. C

D: $

15.9

9 20

. sh

irt:

$25

.50

disc

oun

t: 2

0%

dis

cou

nt:

40%

21. s

leep

ing

bag:

$12

5 22

. cof

fee

mak

er: $

102.

00di

scou

nt:

25%

d

isco

un

t: 4

5%

d

ecre

ase;

60%

incr

ease

; 50

%

d

ecre

ase;

9%

incr

ease

; 12

%

d

ecre

ase;

40%

incr

ease

; 6%

i

ncr

ease

; 25

%

d

ecre

ase;

25%

$

72.4

5

$15.

52

$

30.6

9

$48.

95

$

6.39

$67.

60

$

18.0

2

$51.

60

$

45.0

0

$75.

00

$

12.7

9

$15.

30

$

93.7

5

$56.

10

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4412

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-7

2-7

Prac

tice

Perc

en

t o

f C

han

ge

Cha

pte

r 2

45

Gle

ncoe

Alg

ebra

1

Sta

te w

het

her

eac

h p

erce

nt

of c

han

ge i

s a

per

cen

t of

in

crea

se o

r a

per

cen

t of

d

ecre

ase

. Th

en f

ind

eac

h p

erce

nt

of c

han

ge. R

oun

d t

o th

e n

eare

st w

hol

e p

erce

nt.

1. o

rigi

nal

: 18

2. o

rigi

nal

: 140

3.

ori

gin

al: 2

00n

ew: 1

0 n

ew: 1

60

new

: 320

4. o

rigi

nal

: 10

5. o

rigi

nal

: 76

6. o

rigi

nal

: 128

new

: 25

new

: 60

new

: 120

7. o

rigi

nal

: 15

8. o

rigi

nal

: 98.

6 9.

ori

gin

al: 5

8.8

new

: 35.

5 n

ew: 6

4 n

ew: 6

5.7

Fin

d t

he

tota

l p

rice

of

each

ite

m.

10. c

oncr

ete

bloc

ks: $

95.0

0 11

. cri

b: $

240.

00

12. j

acke

t: $

125.

00ta

x: 6

%

tax

: 6.5

%

tax

: 5.5

%

13. c

lass

rin

g: $

325.

00

14. b

lan

ket:

$24

.99

15. k

ite:

$18

.90

tax:

6%

t

ax: 7

%

tax

: 5%

Fin

d t

he

dis

cou

nte

d p

rice

of

each

ite

m.

16. d

ry c

lean

ing:

$25

.00

17. c

ompu

ter

gam

e: $

49.9

9 18

. lu

ggag

e: $

185.

00di

scou

nt:

15%

d

isco

un

t: 2

5%

dis

cou

nt:

30%

19. s

tati

oner

y: $

12.9

5 20

. pre

scri

ptio

n g

lass

es: $

149

21. p

air

of s

hor

ts: $

24.9

9 di

scou

nt:

10%

d

isco

un

t: 2

0%

d

isco

un

t: 4

5%

Fin

d t

he

fin

al p

rice

of

each

ite

m.

22. t

elev

isio

n: $

375.

00

23. D

VD

pla

yer:

$26

9.00

24

. pri

nte

r: $

255.

00di

scou

nt:

25%

d

isco

un

t: 2

0%

dis

cou

nt:

30%

tax:

6%

t

ax: 7

%

tax

: 5.5

%

25. I

NV

ESTM

ENTS

Th

e pr

ice

per

shar

e of

a s

tock

dec

reas

ed f

rom

$90

per

sh

are

to $

36 p

er

shar

e. B

y w

hat

per

cen

t di

d th

e pr

ice

of t

he

stoc

k de

crea

se?

26. H

EATI

NG

CO

STS

Cu

stom

ers

of a

uti

lity

com

pan

y re

ceiv

ed n

otic

es i

n t

hei

r m

onth

ly

bill

s th

at h

eati

ng

cost

s fo

r th

e av

erag

e cu

stom

er h

ad i

ncr

ease

d 12

5% o

ver

last

yea

r be

cau

se o

f an

un

usu

ally

sev

ere

win

ter.

In J

anu

ary

of l

ast

year

, th

e G

arci

a’s

paid

$12

0 fo

r h

eati

ng.

Wh

at s

hou

ld t

hey

exp

ect

to p

ay t

his

Jan

uar

y if

th

eir

bill

in

crea

sed

by 1

25%

?

d

ecre

ase;

44%

i

ncr

ease

; 14

%

in

crea

se;

60%

i

ncr

ease

; 15

0%

dec

reas

e; 2

1%

dec

reas

e; 6

%

i

ncr

ease

; 13

7%

dec

reas

e; 3

5%

in

crea

se;

12%

$

100.

70

$25

5.60

$

131.

88

$

344.

50

$26

.74

$19

.85

$

21.2

5 $

37.4

9 $

129.

50

$

11.6

6 $

119.

20

$13

.74

$

298.

13

$23

0.26

$

188.

32

60%

$270

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4512

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Wor

d Pr

oble

m P

ract

ice

Perc

en

t o

f C

han

ge

2-7

Cha

pte

r 2

46

Gle

ncoe

Alg

ebra

1

1. S

POR

TS A

reg

ula

tion

gir

ls’ f

ast

pitc

h

soft

ball

dia

mon

d h

as b

ases

th

at a

re

60 f

eet

apar

t. A

reg

ula

tion

pro

fess

ion

al

base

ball

dia

mon

d h

as b

ases

th

at a

re 5

0%

fart

her

apa

rt. L

abel

th

e di

stan

ce

betw

een

th

e ba

ses

on t

he

regu

lati

on

base

ball

dia

mon

d di

agra

m.

2. S

ALE

S TA

X O

livi

a pu

rch

ases

a D

VD

m

ovie

pri

ced

at $

21.9

9. T

he

sale

s ta

x is

6.

5%. W

hat

is

the

tota

l pr

ice

of t

he

mov

ie, i

ncl

udi

ng

tax?

3. E

DU

CA

TIO

N T

he

AC

T i

s a

coll

ege

entr

ance

exa

m t

aken

by

hig

h s

choo

l st

ude

nts

. Th

e m

axim

um

sco

re t

hat

can

be

ear

ned

is

36. T

he

aver

age

scor

e in

th

e U

nit

ed S

tate

s w

as 2

1.2

duri

ng

a re

cen

t ye

ar. T

he

aver

age

scor

e fo

r V

erm

ont

stu

den

ts t

hat

yea

r w

as 7

.5%

hig

her

th

an

the

nat

ion

al a

vera

ge. W

hat

was

th

e av

erag

e A

CT

sco

re f

or V

erm

ont

stu

den

ts?

Rou

nd

you

r an

swer

to

the

nea

rest

ten

th.

4. C

AR

S M

r. T

hom

pson

pla

ns

to p

urc

has

e a

use

d ca

r pr

iced

at

$840

0. H

e w

ill

rece

ive

a 15

% e

mpl

oyee

dis

cou

nt

and

then

wil

l h

ave

to p

ay a

5.5

% s

ales

tax

. W

hat

wil

l be

th

e fi

nal

pri

ce o

f th

e ca

r?

5.M

USI

C T

he t

able

bel

ow s

how

s th

e to

tal

num

ber

of C

Ds,

dow

nloa

ded

sing

les,

and

m

usic

vid

eos

sold

in 2

004,

200

6, a

nd 2

008.

So

urce

: Rec

ordi

ng In

dustr

y As

socia

tion

of A

mer

ica

a. F

ind

the

perc

ent

of c

han

ge i

n t

he

nu

mbe

r of

un

its

sold

bet

wee

n 2

004

and

2006

an

d be

twee

n 2

006

and

2008

fo

r ea

ch f

orm

at. R

oun

d yo

ur

answ

ers

to t

he

nea

rest

ten

th.

b.

Tel

l w

het

her

eac

h p

erce

nt

of c

han

ge

in p

art

a is

a p

erce

nt

of i

ncr

ease

or

a pe

rcen

t of

dec

reas

e.

c. D

id t

hes

e tr

ends

ch

ange

fro

m 2

004

to

2008

? E

xpla

in.

90 ft

90 ft

90 ft

90 ft

Sal

es o

f R

eco

rded

Mu

sic

and

Mu

sic

Vid

eos

(mill

ion

s o

f u

nit

s)

Form

at20

0420

0620

08

CD

767.

061

4.9

368.

4

Dow

nloa

ded

139.

458

6.4

1042

.7

Vid

eo32

.823

.120

.8

$

23.4

2

2

2.8

CD

19

.8%

; 40

.1%

Do

wn

load

ed

320.

6%;

77.8

% V

ideo

29

.6%

; 10

.0%

C

D

dec

reas

e; d

ecre

ase

D

ow

nlo

aded

in

crea

se;

incr

ease

D

VD

vid

eo

incr

ease

; in

crea

se

Th

e C

D s

ales

an

d v

ideo

sal

es

dec

reas

ed in

bo

th t

ime

per

iod

s

and

do

wn

load

ed s

ales

in

crea

sed

bo

th t

ime

per

iod

s.

$

7532

.70

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4612

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-7

Enri

chm

ent

2-7

Cha

pte

r 2

47

Gle

ncoe

Alg

ebra

1

Usin

g P

erc

en

t

Use

wh

at y

ou h

ave

lear

ned

ab

out

per

cen

t to

sol

ve e

ach

pro

ble

m.

A T

V m

ovie

had

a “

rati

ng”

of

15 a

nd

a 25

“sh

are.

” T

he

rati

ng

is t

he

perc

enta

ge o

f th

e n

atio

n’s

tot

al T

V h

ouse

hol

ds t

hat

wer

e tu

ned

in

to

this

sh

ow. T

he

shar

e is

th

e pe

rcen

tage

of

hom

es w

ith

TV

s tu

rned

on

th

at w

ere

tun

ed t

o th

e m

ovie

. How

man

y T

V h

ouse

hol

ds h

ad

thei

r T

Vs

turn

ed o

ff a

t th

is t

ime?

To

fin

d ou

t, l

et T

= t

he

nu

mbe

r of

TV

hou

seh

olds

an

d x

= t

he

nu

mbe

r of

TV

hou

seh

olds

wit

h t

he

TV

off

.

Th

en T

- x

= t

he

nu

mbe

r of

TV

hou

seh

olds

wit

h t

he

TV

on

.S

ince

0.1

5T a

nd

0.25

(T -

x)

both

rep

rese

nt

the

nu

mbe

r of

hou

seh

olds

tu

ned

to

th

e m

ovie

,

0.15

T =

0.2

5(T

- x

)

0.15

T =

0.2

5T -

0.2

5x.

Sol

ve f

or x

. 0.

25x

= 0

.10T

x

= 0.

10T

−

0.25

or

0.4

0T

For

ty p

erce

nt

of t

he

TV

hou

seh

olds

had

th

eir

TV

s of

f w

hen

th

e m

ovie

was

air

ed.

An

swer

eac

h q

ues

tion

.

1. D

urin

g th

at s

ame

wee

k, a

spo

rts

broa

dcas

t ha

d a

rati

ng o

f 22

.1 a

nd a

43

shar

e. S

how

tha

t th

e pe

rcen

t of

TV

hou

seho

lds

wit

h th

eir

TV

s of

f w

as a

bout

48.

6%.

2. F

ind

the

perc

ent

of T

V h

ouse

hol

ds w

ith

th

eir

TV

s tu

rned

off

du

rin

g a

show

w

ith

a r

atin

g of

18.

9 an

d a

29 s

har

e.

3. S

how

th

at i

f T

is

the

nu

mbe

r of

TV

hou

seh

olds

, r i

s th

e ra

tin

g, a

nd

s is

th

e

sh

are,

th

en t

he

nu

mbe

r of

TV

hou

seh

olds

wit

h t

he

TV

off

is

(s -

r)T

−

s .

4. I

f th

e fr

acti

on o

f TV

hou

seh

olds

wit

h n

o T

V o

n i

s s

- r

−

s t

hen

sh

ow t

hat

th

e

frac

tion

of T

V h

ouse

hol

ds w

ith

TV

s on

is

r −

s .

5. F

ind

the

perc

ent

of T

V h

ouse

hol

ds w

ith

TV

s on

du

rin

g th

e m

ost

wat

ched

se

rial

pro

gram

in

his

tory

: th

e la

st e

piso

de o

f M

*A*S

*H, w

hic

h h

ad a

60.

3 ra

tin

g an

d a

77 s

har

e.

6. A

loc

al s

tati

on n

ow h

as a

2 s

har

e. E

ach

sh

are

is w

orth

$50

,000

in

adv

erti

sin

g re

ven

ue

per

mon

th. T

he

stat

ion

is

thin

kin

g of

goi

ng

com

mer

cial

fre

e fo

r th

e th

ree

mon

ths

of s

um

mer

to

gain

mor

e li

sten

ers.

Wh

at w

ould

its

new

sh

are

hav

e to

be

for

the

last

4 m

onth

s of

th

e ye

ar t

o m

ake

mor

e m

oney

for

th

e ye

ar

than

it

wou

ld h

ave

mad

e h

ad i

t n

ot g

one

com

mer

cial

fre

e?

0

.221

T =

0.4

3T -

0.4

3x

x =

0.

221T

- 0.

43T

−

-0.

43

= 0

.486

T

34.8

%

So

lve

rT =

s(T

- x

) fo

r x.

60.3

−

77

= 7

8.3%

gre

ater

th

an 3

.5

1 -

s

-

r

−

s

= r −

s

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4712

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Spre

adsh

eet

Act

ivit

yD

isco

un

ts

2-7

Cha

pte

r 2

48

Gle

ncoe

Alg

ebra

1

Exer

cise

s 1

. For

th

e se

con

d w

eek

of t

he

sale

, th

e E

lect

ron

ics

War

ehou

se m

anag

er i

s ch

angi

ng

the

disc

oun

ts t

o 20

%, 3

0%, 4

5%, a

nd

75%

off

. Use

a s

prea

dsh

eet

to c

reat

e a

new

dis

coun

t pr

ice

list

for

the

sof

twar

e.

2. H

ow s

hou

ld t

he

spre

adsh

eet

be a

lter

ed i

f th

e m

anag

er w

ish

ed t

o sh

ow t

he

fin

al p

rice

s of

th

e so

ftw

are

incl

udi

ng

the

6% s

ales

tax

for

th

eir

area

?

Ele

ctro

nic

s W

areh

ouse

is

hav

ing

a so

ftw

are

clea

ran

ce s

ale.

Th

e m

anag

er i

s m

akin

g a

dis

cou

nte

d p

rice

lis

t to

dis

trib

ute

to

cust

omer

s as

th

ey s

hop

. Dif

fere

nt

tab

les

wil

l h

ave

soft

war

e th

at i

s d

isco

un

ted

by

a d

iffe

ren

t p

erce

nt.

Use

a s

pre

adsh

eet

to s

how

th

e d

isco

un

ted

pri

ce o

f so

ftw

are

that

is

orig

inal

ly p

rice

d $

5.99

, $7.

99, $

9.99

, $15

.99,

$1

9.99

, $23

.99,

$27

.99,

$29

.99,

$33

.99,

an

d $

35.9

9. C

omp

ute

dis

cou

nte

d p

rice

s fo

r so

ftw

are

that

is

10%

, 15%

, 25%

, an

d 5

0% o

ff.

If a

n i

tem

is

on s

ale

for

10%

off

, th

at m

ean

s th

at d

isco

un

ted

pric

e is

(1

- 0

.1)

or 0

.9 t

imes

th

e or

igin

al p

rice

. Use

th

is p

atte

rn t

o co

mpl

ete

the

spre

adsh

eet.

Ste

p 1

U

se C

olu

mn

A o

f th

e sp

read

shee

t fo

r th

e or

igin

al p

rice

s.

Ste

p 2

C

olu

mn

s B

th

rou

gh E

con

tain

th

e fo

rmu

las

for

the

disc

oun

ted

pric

es.

Ste

p 3

B

ecau

se t

hes

e ar

e pr

ices

, th

e n

um

bers

mu

st b

e ro

un

ded

to 2

dig

its.

You

can

pr

ogra

m t

he

spre

adsh

eet

to l

ist

the

info

rmat

ion

as

doll

ars

and

cen

ts b

y ch

oosi

ng

curr

ency

fro

m t

he

nu

mbe

r m

enu

wh

en y

ou f

orm

at t

he

cell

s.

Dis

cou

nts

.xls

A1 3 4 5 6 7 8 9 10 112

BC

DE

12S

hee

t 1

Sh

eet

2S

hee

t 3

The

form

ula

ince

ll C

11 is

0.8

5*A1

1

The

form

ula

ince

ll E6

is 0

.5*A

6

Orig

inal

pric

e10

% o

ff15

% o

ff25

% o

ff50

% o

ff

$5.9

9$7

.99

$9.9

9$1

5.99

$19.

99$2

3.99

$27.

99$2

9.99

$33.

99$3

5.99

$5.3

9$7

.19

$8.9

9$1

4.39

$17.

99$2

1.59

$25.

19$2

6.99

$30.

59$3

2.39

$5.0

9$8

.79

$8.4

9$1

3.59

$16.

99$2

0.39

$23.

79$2

5.49

$28.

89$3

0.59

$3.0

0$4

.00

$5.0

0$8

.00

$10.

00$1

2.00

$14.

00$1

5.00

$17.

00$1

8.00

$4.4

9$5

.99

$7.4

9$1

1.99

$14.

99$1

7.99

$20.

99$2

2.49

$25.

49$2

6.99

See

stu

den

ts’ w

ork

.

Mu

ltip

ly e

ach

dis

cou

nte

d p

rice

by

1.06

.

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4812

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-8

2-8

Stud

y G

uide

and

Inte

rven

tion

Lit

era

l E

qu

ati

on

s a

nd

Dim

en

sio

nal A

naly

sis

Cha

pte

r 2

49

Gle

ncoe

Alg

ebra

1

Solv

e fo

r V

aria

ble

s S

omet

imes

you

may

wan

t to

sol

ve a

n e

quat

ion

su

ch a

s V

= �

wh

for

on

e of

its

var

iabl

es. F

or e

xam

ple,

if

you

kn

ow t

he

valu

es o

f V

, w, a

nd

h, t

hen

th

e eq

uat

ion

� =

V

−

wh i

s m

ore

use

ful

for

fin

din

g th

e va

lue

of �

. If

an e

quat

ion

th

at c

onta

ins

mor

e th

an o

ne

vari

able

is

to b

e so

lved

for

a s

peci

fic

vari

able

, use

th

e pr

oper

ties

of

equ

alit

y to

iso

late

th

e sp

ecif

ied

vari

able

on

on

e si

de o

f th

e eq

uat

ion

.

S

olve

2x

- 4

y =

8, f

or y

.

2x

- 4

y =

8 2x

- 4

y -

2x

= 8

- 2

x

-4y

= 8

- 2

x

-

4y

−

-4 =

8 -

2x

−

-4

y

= 8

- 2

x −

-

4

or

2x -

8

−

4

Th

e va

lue

of y

is

2x -

8

−

4 .

S

olve

3m

- n

= k

m -

8, f

or m

.

3m

- n

= k

m -

8

3m -

n -

km

= k

m -

8 -

km

3m

- n

- k

m =

- 8

3m -

n -

km

+ n

= -

8 +

n

3m -

km

= -

8 +

n

m(3

- k

) =

-8

+ n

m

(3 -

k)

−

3 -

k =

-8

+ n

−

3 -

k

m

= -

8 +

n

−

3 -

k

or

n -

8

−

3 -

k

The

val

ue o

f m

is n

- 8

−

3 -

k .

Sin

ce d

ivis

ion

by 0

is

un

defi

ned

, 3 -

k ≠

0, o

r k

≠ 3

.

Exer

cise

s S

olve

eac

h e

qu

atio

n o

r fo

rmu

la f

or t

he

vari

able

in

dic

ated

.

1. a

x -

b =

c, f

or x

2.

15x

+ 1

= y

, for

x

3. (

x +

f)

+ 2

= j

, for

x

4. x

y +

w =

9, f

or y

5.

x(4

- k

) =

p, f

or k

6.

7x

+ 3

y =

m, f

or y

7. 4

(r +

3)

= t

, for

r

8. 2

x +

b =

w, f

or x

9.

x(1

+ y

) =

z, f

or x

10. 1

6w +

4x

= y

, for

x

11. d

= r

t, f

or r

12

. A =

h(a

+ b

) −

2

, fo

r h

13. C

= 5 −

9 (F

- 3

2), f

or F

14

. P =

2� +

2w

, for

w

15. A

= �

w, f

or �

Exam

ple

2Ex

amp

le 1

x

= c

+ b

−

a

, a ≠

0

x =

y -

1

−

15

x

= j

- 2

- f

y

= 9

- w

−

x

, x ≠

0

k =

4 -

p

−

x ,

x ≠

0

y =

m -

7x

−

3

r

= t −

4 - 3

x

= w

- b

−

2

x =

z

−

1 +

y ,

y ≠

-1

x

= y

- 1

6w

−

4

r =

d

−

t , t

≠ 0

h

=

2A

−

a +

b ,

a ≠

-b

F

= 9

−

5 C +

32

W =

p -

2�

−

2

� =

A

−

w ,

w ≠

0

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

4912

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Lit

era

l E

qu

ati

on

s a

nd

Dim

en

sio

nal A

naly

sis

2-8

Cha

pte

r 2

50

Gle

ncoe

Alg

ebra

1

Use

Fo

rmu

las

Man

y re

al-w

orld

pro

blem

s re

quir

e th

e u

se o

f fo

rmu

las.

Som

etim

es s

olvi

ng

a fo

rmu

la f

or a

spe

cifi

ed v

aria

ble

wil

l h

elp

solv

e th

e pr

oble

m.

T

he

form

ula

C =

πd

rep

rese

nts

th

e ci

rcu

mfe

ren

ce o

f a

circ

le, o

r th

e d

ista

nce

aro

un

d t

he

circ

le, w

her

e d

is

the

dia

met

er. I

f an

air

pla

ne

cou

ld f

ly a

rou

nd

E

arth

at

the

equ

ator

wit

hou

t st

opp

ing,

it

wou

ld h

ave

trav

eled

ab

out

24,9

00 m

iles

. F

ind

th

e d

iam

eter

of

Ear

th.

C =

πd

G

iven

form

ula

d =

C

−

π

Sol

ve fo

r d

.

d =

24,9

00

−

3.14

Use

π =

3.1

4.

d ≈

793

0 S

impl

ify.

Th

e di

amet

er o

f E

arth

is

abou

t 79

30 m

iles

.

Exer

cise

s 1

. GEO

MET

RY T

he

volu

me

of a

cyl

inde

r V

is

give

n b

y th

e fo

rmu

la V

= π

r2 h, w

her

e r

is

the

radi

us

and

h i

s th

e h

eigh

t.

a. S

olve

th

e fo

rmu

la f

or h

.

b.

Fin

d th

e h

eigh

t of

a c

ylin

der

wit

h v

olu

me

2500

π c

ubi

c fe

et a

nd

radi

us

10 f

eet.

2. W

ATE

R P

RES

SUR

E T

he

wat

er p

ress

ure

on

a s

ubm

erge

d ob

ject

is

give

n b

y P

= 6

4d,

wh

ere

P i

s th

e pr

essu

re i

n p

oun

ds p

er s

quar

e fo

ot, a

nd

d i

s th

e de

pth

of

the

obje

ct

in f

eet.

a. S

olve

th

e fo

rmu

la f

or d

.

b.

Fin

d th

e de

pth

of a

sub

mer

ged

obje

ct if

the

pre

ssur

e is

672

pou

nds

per

squa

re f

oot.

3. G

RA

PHS

Th

e eq

uat

ion

of

a li

ne

con

tain

ing

the

poin

ts (

a, 0

) an

d (0

, b)

is g

iven

by

the

fo

rmu

la x −

a

+ y −

b =

1.

a. S

olve

th

e eq

uat

ion

for

y.

b.

Su

ppos

e th

e li

ne

con

tain

s th

e po

ints

(4,

0),

and

(0, -

2). I

f x

= 3

, fin

d y.

4. G

EOM

ETRY

Th

e su

rfac

e ar

ea o

f a

rect

angu

lar

soli

d is

giv

en b

y th

e fo

rmu

la

x =

2�w

+ 2

�h

+ 2

wh

, wh

ere

� =

len

gth

, w =

wid

th, a

nd

h =

hei

ght.

a. S

olve

th

e fo

rmu

la f

or h

.

b.

Th

e su

rfac

e ar

ea o

f a

rect

angu

lar

soli

d w

ith

len

gth

6 c

enti

met

ers

and

wid

th

3 ce

nti

met

ers

is 7

2 sq

uar

e ce

nti

met

ers.

Fin

d th

e h

eigh

t.

Exam

ple

25 f

t

10.5

ft

2 cm

h =

V

−

πr2

d =

p

−

64

y =

b (1

- x

−

a )

- 1 −

2

h =

x

- 2

�w

−

2� +

2w

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5012

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-8

Skill

s Pr

acti

ceLit

era

l E

qu

ati

on

s a

nd

Dim

en

sio

nal A

naly

sis

2-8

Cha

pte

r 2

51

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

eq

uat

ion

or

form

ula

for

th

e va

riab

le i

nd

icat

ed.

1. 7

t =

x, f

or t

2.

r =

wp,

for

p

3. q

- r

= r

, for

r

4. 4

m -

t =

m, f

or m

5. 7

a -

b =

15a

, for

a

6. -

5c +

d =

2c,

for

c

7. x

- 2

y =

1, f

or y

8.

d +

3n

= 1

, for

n

9. 7

f +

g =

5, f

or f

10

. ax

- c

= b

, for

x

11. r

t -

2n

= y

, for

t

12. b

c +

3g

= 2

k, f

or c

13. k

n +

4f

= 9

v, f

or n

14

. 8c

+ 6

j =

5p,

for

c

15.

x -

c

−

2 =

d, f

or x

16

. x

- c

−

2 =

d, f

or c

17.

p +

9

−

5 =

r, f

or p

18

. b

- 4

z −

7

= a

, for

b

19. T

he

volu

me

of a

box

V i

s gi

ven

by

the

form

ula

V =

ℓw

h, w

her

e ℓ

is t

he

len

gth

, w

is

the

wid

th, a

nd

h i

s th

e h

eigh

t.

a. S

olve

th

e fo

rmu

la f

or h

.

b.

Wh

at i

s th

e h

eigh

t of

a b

ox w

ith

a v

olu

me

of 5

0 cu

bic

met

ers,

len

gth

of

10 m

eter

s,

and

wid

th o

f 2

met

ers?

20. T

ren

t pu

rch

ases

44

euro

s w

orth

of

sou

ven

irs

wh

ile

on v

acat

ion

in

Fra

nce

. If

$1

U.S

. = 0

.678

eu

ros,

fin

d th

e co

st o

f th

e so

uve

nir

s in

Un

ited

Sta

tes

doll

ars.

R

oun

d to

th

e n

eare

st c

ent.

t =

x

−

7 p

=

r −

w

r =

q

−

2 m

= t −

3

a =

- b

−

8

c =

d

−

7

y =

x -

1

−

2 n

= 1

- d

−

3

f =

5 -

g

−

7

x =

b +

c

−

a

; a ≠

0

t =

2n +

y

−

r ;

r ≠

0

n =

9v -

4f

−

k

; k ≠

0

c =

2k -

3g

−

b

; b

≠ 0

c =

5p -

6j

−

8

x =

c +

2d

p =

5r

- 9

c =

x -

2d

b =

7a +

4z

h =

V

−

ℓw

2.5

m

$64.

90

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5112

/23/

10

12:0

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF 2nd



NA

ME

DAT

E

P

ER

IOD

Prac

tice

Lit

era

l E

qu

ati

on

s a

nd

Dim

en

sio

nal A

naly

sis

2-8

Cha

pte

r 2

52

Gle

ncoe

Alg

ebra

1

Sol

ve e

ach

eq

uat

ion

or

form

ula

for

th

e va

riab

le i

nd

icat

ed.

1. d

= r

t, fo

r r

2.

6w

- y

= 2

z, f

or w

3. m

x +

4y

= 3

t, fo

r x

4.

9s

- 5

g =

-4u

, for

s

5. a

b +

3c

= 2

x, f

or b

6.

2p

= k

x -

t, f

or x

7.

2 −

3 m

+ a

= a

+ r

, for

m

8. 2 −

5 h

+ g

= d

, for

h

9.

2 −

3 y

+ v

= x

, for

y

10.

3 −

4 a

- q

= k

, for

a

11.

rx +

9

−

5 =

h, f

or x

12

. 3b

- 4

−

2 =

c, f

or b

13. 2

w -

y =

7w

- 2

, for

w

14. 3

� +

y =

5 +

5�, f

or �

15. E

LEC

TRIC

ITY

Th

e fo

rmu

la f

or O

hm

’s L

aw i

s E

= I

R, w

her

e E

rep

rese

nts

vol

tage

m

easu

red

in v

olts

, I r

epre

sen

ts c

urr

ent

mea

sure

d in

am

pere

s, a

nd

R r

epre

sen

ts

resi

stan

ce m

easu

red

in o

hm

s.

a. S

olve

th

e fo

rmu

la f

or R

.

b.

Su

ppos

e a

curr

ent

of 0

.25

ampe

re f

low

s th

rou

gh a

res

isto

r co

nn

ecte

d to

a 1

2-vo

lt

batt

ery.

Wh

at i

s th

e re

sist

ance

in

th

e ci

rcu

it?

16. M

OTI

ON

In

un

ifor

m c

ircu

lar

mot

ion

, th

e sp

eed

v of

a p

oin

t on

th

e ed

ge o

f a

spin

nin

g di

sk i

s v

= 2π

−

t

r, w

her

e r

is t

he

radi

us

of t

he

disk

an

d t

is t

he

tim

e it

tak

es t

he

poin

t to

tr

avel

on

ce a

rou

nd

the

circ

le.

a. S

olve

th

e fo

rmu

la f

or r

.

b.

Su

ppos

e a

mer

ry-g

o-ro

un

d is

spi

nn

ing

once

eve

ry 3

sec

onds

. If

a po

int

on t

he

outs

ide

edge

has

a s

peed

of

12.5

6 fe

et p

er s

econ

d, w

hat

is

the

radi

us

of t

he

mer

ry-g

o-ro

un

d?

(Use

3.1

4 fo

r π

.)

17. H

IGH

WA

YS

Inte

rsta

te 9

0 is

th

e lo

nge

st i

nte

rsta

te h

igh

way

in

th

e U

nit

ed S

tate

s,

con

nec

tin

g th

e ci

ties

of

Sea

ttle

, Was

hin

gton

an

d B

osto

n, M

assa

chu

sett

s. T

he

inte

rsta

te

is 4

,987

,000

met

ers

in l

engt

h. I

f 1

mil

e =

1.6

09 k

ilom

eter

s, h

ow m

any

mil

es l

ong

is

Inte

rsta

te 9

0?

48 o

hm

s

6 ft

r =

d

−

t w

= 2z

+ y

−

6

x =

3t

- 4

y

−

m

; m

≠ 0

s =

-

4u +

5g

−

9

b =

2x

- 3

c

−

a

; a ≠

0x =

2p

+ t

−

k

; k ≠

0

m =

3 −

2 rh

= 5 −

2 (d

- g

)

y =

3 −

2 (x -

v)

a =

4 −

3 (k +

q)

x =

5h

- 9

−

r ;

r ≠

0b

= 2c

+ 4

−

3

w =

2

- y

−

5

ℓ =

y

- 5

−

2

R =

E

−

I

r =

tv

−

2π

3099

mi

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5212

/23/

10

12:1

3 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-8

Wor

d Pr

oble

m P

ract

ice

Lit

era

l E

qu

ati

on

s a

nd

Dim

en

sio

nal A

naly

sis

2-8

Cha

pte

r 2

53

Gle

ncoe

Alg

ebra

1

1. IN

TER

EST

Sim

ple

inte

rest

th

at y

ou m

ay

earn

on

mon

ey i

n a

sav

ings

ac

cou

nt

can

be

calc

ula

ted

wit

h t

he

form

ula

I=

prt.

I is

th

e am

oun

t of

in

tere

st e

arn

ed, p

is

the

prin

cipa

l or

in

itia

l am

oun

t in

vest

ed, r

is

the

inte

rest

ra

te, a

nd

t is

th

e am

oun

t of

tim

e th

e m

oney

is

inve

sted

for

. Sol

ve t

he

form

ula

fo

r p.

2. D

ISTA

NC

E T

he

dist

ance

d a

car

can

tr

avel

is

fou

nd

by m

ult

iply

ing

its

rate

of

spee

d r

by t

he

amou

nt

of t

ime

t th

at i

t to

ok t

o tr

avel

th

e di

stan

ce. I

f a

car

has

al

read

y tr

avel

ed 5

mil

es, t

he

tota

l di

stan

ce d

is

fou

nd

by t

he

form

ula

d

= r

t + 5

. S

olve

th

e fo

rmu

la f

or r

.

3. E

NV

IRO

NM

ENT

Th

e U

nit

ed S

tate

s re

leas

ed 5

.877

bil

lion

met

ric

ton

s of

ca

rbon

dio

xide

in

to t

he

envi

ron

men

t th

rou

gh t

he

burn

ing

of f

ossi

l fu

els

in a

re

cen

t ye

ar. I

f 1

tril

lion

pou

nds

= 0

.453

6 bi

llio

n m

etri

c to

ns,

how

man

y tr

illi

ons

of

pou

nds

of

carb

on d

ioxi

de d

id t

he

Un

ited

S

tate

s re

leas

e in

th

at y

ear?

4. P

HY

SIC

S T

he

pres

sure

exe

rted

on

an

obj

ect

is c

alcu

late

d by

th

e fo

rmu

la

P =

F − A, w

her

e P

is

the

pres

sure

, F i

s th

e fo

rce,

an

d A

is

the

surf

ace

area

of

the

obje

ct. W

ater

sh

ooti

ng

from

a h

ose

has

a

pres

sure

of

75 p

oun

ds p

er s

quar

e in

ch

(psi

). S

upp

ose

the

surf

ace

area

cov

ered

by

th

e di

rect

hos

e sp

ray

is 0

.442

squ

are

inch

. Sol

ve t

he

equ

atio

n f

or F

an

d fi

nd

the

forc

e of

th

e sp

ray.

5. G

EOM

ETRY

Th

e re

gula

r oc

tago

n i

s di

vide

d in

to 8

con

gru

ent

tria

ngl

es. E

ach

tr

ian

gle

has

an

are

a of

21.

7 sq

uar

e ce

nti

met

ers.

Th

e pe

rim

eter

of

the

octa

gon

is

48 c

enti

met

ers.

a. W

hat

is

the

len

gth

of

each

sid

e of

th

e oc

tago

n?

b. S

olve

the

are

a of

a t

rian

gle

form

ula

for

h.

c. W

hat

is

the

hei

ght

of e

ach

tri

angl

e?

Rou

nd

to t

he

nea

rest

ten

th.

h

≈

12.9

6

3

3.15

po

un

ds

6 ce

nti

met

ers

7.2

cen

tim

eter

s

p =

I −

rt

r =

d -

5

−

t

h =

2A

−

b

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5312

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-8

Cha

pte

r 2

54

Gle

ncoe

Alg

ebra

1

Co

mp

ou

nd

Inte

rest

In m

ost

ban

ks, i

nte

rest

on

sav

ings

acc

oun

ts i

s co

mpo

un

ded

at s

et t

ime

peri

ods

such

as

thre

e or

six

mon

ths.

At

the

end

of e

ach

per

iod,

th

e ba

nk

adds

th

e in

tere

st e

arn

ed t

o th

e ac

cou

nt.

Du

rin

g th

e n

ext

peri

od,

the

ban

k pa

ys i

nte

rest

on

all

th

e m

oney

in

th

e ba

nk,

in

clu

din

g in

tere

st.

In t

his

way

, th

e ac

cou

nt

earn

s in

tere

st o

n i

nte

rest

.S

upp

ose

Ms.

Tan

ner

has

$10

00 i

n a

n a

ccou

nt

that

is

com

pou

nde

d qu

arte

rly

at 5

%. F

ind

the

bala

nce

aft

er t

he

firs

t tw

o qu

arte

rs.

Use

I =

prt

to

fin

d th

e in

tere

st e

arn

ed i

n t

he

firs

t qu

arte

r if

p =

100

0

and

r =

5%

. Wh

y is

t e

qual

to

1 −

4 ?

Fir

st q

uar

ter:

I

= 1

000

× 0

.05

× 1 −

4

I =

12.

50

Th

e in

tere

st, $

12.5

0, e

arn

ed i

n t

he

firs

t qu

arte

r is

add

ed t

o $1

000.

T

he

prin

cipa

l be

com

es $

1012

.50.

Sec

ond

quar

ter:

I =

101

2.50

× 0

.05

× 1 −

4

I

= 1

2.65

625

Th

e in

tere

st i

n t

he

seco

nd

quar

ter

is $

12.6

6.

Th

e ba

lan

ce a

fter

tw

o qu

arte

rs i

s $1

012.

50 +

12.

66 o

r $1

025.

16.

An

swer

eac

h o

f th

e fo

llow

ing

qu

esti

ons.

1. H

ow m

uch

in

tere

st i

s ea

rned

in

th

e th

ird

quar

ter

of M

s. T

ann

er’s

ac

cou

nt?

2. W

hat

is

the

bala

nce

in

her

acc

oun

t af

ter

thre

e qu

arte

rs?

3. H

ow m

uch

in

tere

st i

s ea

rned

in

th

e fo

urt

h q

uar

ter?

4. W

hat

is

the

bala

nce

in

her

acc

oun

t af

ter

one

year

?

5. S

upp

ose

Ms.

Tan

ner

’s a

ccou

nt

is c

ompo

un

ded

sem

ian

nu

ally

. Wh

at

is t

he

bala

nce

at

the

end

of s

ix m

onth

s?

6. W

hat

is

the

bala

nce

aft

er o

ne

year

if

her

acc

oun

t is

com

pou

nde

d se

mia

nn

ual

ly?

I = $

12.8

1

$103

7.97

I = $

12.9

7

$105

0.94

$102

5.0

0

$105

0.63

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5412

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-9

Stud

y G

uide

and

Inte

rven

tion

Weig

hte

d A

vera

ges

2-9

Cha

pte

r 2

55

Gle

ncoe

Alg

ebra

1

Mix

ture

Pro

ble

ms

Mix

ture

Pro

ble

ms

are

prob

lem

s w

her

e tw

o or

mor

e pa

rts

are

com

bin

ed i

nto

a w

hol

e. T

hey

in

volv

e w

eigh

ted

aver

ages

. In

a m

ixtu

re p

robl

em, t

he

wei

ght

is

usu

ally

a p

rice

or

a pe

rcen

t of

som

eth

ing.

Wei

gh

ted

Ave

rag

eT

he w

eigh

ted

aver

age

M o

f a

set

of d

ata

is t

he s

um o

f th

e pr

oduc

t of

eac

h nu

mbe

r in

the

set

an

d its

wei

ght

divi

ded

by t

he s

um o

f al

l the

wei

ghts

.

C

OO

KIE

S D

elec

tab

le C

ook

ie C

omp

any

sell

s ch

ocol

ate

chip

coo

kie

s fo

r $6

.95

per

pou

nd

an

d w

hit

e ch

ocol

ate

cook

ies

for

$5.9

5 p

er p

oun

d. H

ow m

any

pou

nd

s of

ch

ocol

ate

chip

coo

kie

s sh

ould

be

mix

ed w

ith

4 p

oun

ds

of w

hit

e ch

ocol

ate

cook

ies

to o

bta

in a

mix

ture

th

at s

ells

for

$6.

75 p

er p

oun

d.

Let

w =

th

e n

um

ber

of p

oun

ds o

f ch

ocol

ate

chip

coo

kies

Nu

mb

er o

f P

ou

nd

sP

rice

per

Po

un

dTo

tal P

rice

Ch

oco

late

Ch

ipw

6.95

6.95

wW

hit

e C

ho

cola

te4

5.95

4(5.

95)

Mix

ture

w +

46.

756.

75(w

+ 4

)

Equ

atio

n: 6

.95w

+ 4

(5.9

5) =

6.7

5(w

+ 4

)S

olve

th

e eq

uat

ion

.

6.95

w +

4(5

.95)

= 6

.75(

w +

4)

Orig

inal

equ

atio

n

6.

95w

+ 2

3.80

= 6

.75w

+ 2

7 S

impl

ify.

6.95

w +

23.

80 -

6.7

5w =

6.7

5w +

27

- 6

.75w

S

ubtr

act

6.75

w f

rom

eac

h si

de.

0.

2w +

23.

80 =

27

Sim

plify

.

0.

2w +

23.

80 -

23.

80 =

27

- 2

3.80

S

ubtr

act

23.8

0 fr

om e

ach

side

.

0.

2w =

3.2

S

impl

ify.

w

= 1

6 S

impl

ify.

16 p

ound

s of

cho

cola

te c

hip

cook

ies

shou

ld b

e m

ixed

wit

h 4

poun

ds o

f w

hite

cho

cola

te c

ooki

es.

Exer

cise

s 1

. SO

LUTI

ON

S H

ow m

any

gram

s of

su

gar

mu

st b

e ad

ded

to 6

0 gr

ams

of a

sol

uti

on t

hat

is

32%

su

gar

to o

btai

n a

sol

uti

on t

hat

is

50%

su

gar?

2. N

UTS

Th

e Q

uik

Mar

t h

as t

wo

kin

ds o

f n

uts

. Pec

ans

sell

for

$1.

55 p

er p

oun

d an

d w

aln

uts

sel

l fo

r $1

.95

per

pou

nd.

How

man

y po

un

ds o

f w

aln

uts

mu

st b

e ad

ded

to 1

5 po

un

ds o

f pe

can

s to

mak

e a

mix

ture

th

at s

ells

for

$1.

75 p

er p

oun

d?

3. I

NV

ESTM

ENTS

Ali

ce G

leas

on i

nve

sted

a p

orti

on o

f $3

2,00

0 at

9%

in

tere

st a

nd

the

bala

nce

at

11%

in

tere

st. H

ow m

uch

did

sh

e in

vest

at

each

rat

e if

her

tot

al i

nco

me

from

bo

th i

nve

stm

ents

was

$32

00.

4. M

ILK

Wh

ole

mil

k is

4%

bu

tter

fat.

How

mu

ch s

kim

mil

k w

ith

0%

bu

tter

fat

shou

ld b

e ad

ded

to 3

2 ou

nce

s of

wh

ole

mil

k to

obt

ain

a m

ixtu

re t

hat

is

2.5%

bu

tter

fat?

Exam

ple

21.6

g

15 lb

$16,

00

0 at

9%

an

d $

16,0

00

at 1

1%

19.2

oz

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5512

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

2-9

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Weig

hte

d A

vera

ges

Cha

pte

r 2

56

Gle

ncoe

Alg

ebra

1

Un

ifo

rm M

oti

on

Pro

ble

ms

Mot

ion

pro

blem

s ar

e an

oth

er a

ppli

cati

on o

f w

eigh

ted

aver

ages

. Un

ifor

m m

otio

n p

rob

lem

s ar

e pr

oble

ms

wh

ere

an o

bjec

t m

oves

at

a ce

rtai

n

spee

d, o

r ra

te. U

se t

he

form

ula

d =

rt

to s

olve

th

ese

prob

lem

s, w

her

e d

is

the

dist

ance

, r i

s th

e ra

te, a

nd

t is

th

e ti

me.

DR

IVIN

G B

ill

Gu

tier

rez

dro

ve a

t a

spee

d o

f 65

mil

es p

er h

our

on a

n

exp

ress

way

for

2 h

ours

. He

then

dro

ve f

or 1

.5 h

ours

at

a sp

eed

of

45 m

iles

per

h

our

on a

sta

te h

igh

way

. Wh

at w

as h

is a

vera

ge s

pee

d?

M =

65 .

2 +

45

. 1.5

−

2

+ 1

.5

D

efi n

ition

of

wei

ghte

d av

erag

e

≈ 5

6.4

Sim

plify

.

Bil

l dr

ove

at a

n a

vera

ge s

peed

of

abou

t 56

.4 m

iles

per

hou

r.

Exer

cise

s 1

. TR

AV

EL M

r. A

nde

rs a

nd

Ms.

Ric

h e

ach

dro

ve h

ome

from

a b

usi

nes

s m

eeti

ng.

M

r. A

nde

rs t

rave

led

east

at

100

kilo

met

ers

per

hou

r an

d M

s. R

ich

tra

vele

d w

est

at 8

0 ki

lom

eter

s pe

r h

ours

. In

how

man

y h

ours

wer

e th

ey 1

00 k

ilom

eter

s ap

art.

2. A

IRPL

AN

ES A

n a

irpl

ane

flie

s 75

0 m

iles

du

e w

est

in 1

1 −

2 h

ours

an

d 75

0 m

iles

du

e so

uth

in

2 h

ours

. Wh

at i

s th

e av

erag

e sp

eed

of t

he

airp

lan

e?

3. T

RA

CK

Spr

inte

r A

ru

ns

100

met

ers

in 1

5 se

con

ds, w

hil

e sp

rin

ter

B s

tart

s 1.

5 se

con

ds

late

r an

d ru

ns

100

met

ers

in 1

4 se

con

ds. I

f ea

ch o

f th

em r

un

s at

a c

onst

ant

rate

, wh

o is

fu

rth

er i

n 1

0 se

con

ds a

fter

th

e st

art

of t

he

race

? E

xpla

in.

4. T

RA

INS

An

exp

ress

tra

in t

rave

ls 9

0 ki

lom

eter

s pe

r h

our

from

Sm

allv

ille

to

Meg

atow

n.

A l

ocal

tra

in t

akes

2.5

hou

rs l

onge

r to

tra

vel

the

sam

e di

stan

ce a

t 50

kil

omet

ers

per

hou

r. H

ow f

ar a

part

are

Sm

allv

ille

an

d M

egat

own

?

5. C

YC

LIN

G T

wo

cycl

ists

beg

in t

rave

lin

g in

th

e sa

me

dire

ctio

n o

n t

he

sam

e bi

ke p

ath

. On

e tr

avel

s at

15

mil

es p

er h

our,

and

the

oth

er t

rave

ls a

t 12

mil

es p

er h

our.

Wh

en w

ill

the

cycl

ists

be

10 m

iles

apa

rt?

6. T

RA

INS

Tw

o tr

ain

s le

ave

Ch

icag

o, o

ne

trav

elin

g ea

st a

t 30

mil

es p

er h

our

and

one

trav

elin

g w

est

at 4

0 m

iles

per

hou

r. W

hen

wil

l th

e tr

ain

s be

210

mil

es a

part

?

Exam

ple

5 −

9 h

abo

ut

429

mp

h

S

pri

nte

r A

; si

nce

sp

rin

ter

A r

un

s 10

0 m

in 1

5 s,

th

is s

pri

nte

r ru

ns

at a

r

ate

of

100

−

15

m/s

. In

10

seco

nd

s, s

pri

nte

r A

will

hav

e ru

n 10

0 −

15

(10)

= 6

6.7

m.

S

pri

nte

r B

’s r

ate

is 10

0 −

14

. In

10

seco

nd

s, w

ith

th

e d

elay

ed s

tart

, sp

rin

ter

B

h

as r

un

100

−

14

(10

- 1

.5)

= 6

0.7

m.

281.

25 k

m

3 h

3 1 −

3 h

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5612

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-9

Skill

s Pr

acti

ceW

eig

hte

d A

vera

ges

2-9

Cha

pte

r 2

57

Gle

ncoe

Alg

ebra

1

1.SE

ASO

NIN

G A

hea

lth

foo

d st

ore

sell

s se

ason

ing

blen

ds i

n b

ulk

. On

e bl

end

con

tain

s 20

% b

asil

. Sh

eila

wan

ts t

o ad

d pu

re b

asil

to

som

e 20

% b

len

d to

mak

e 16

ou

nce

s of

her

ow

n 3

0% b

len

d. L

et b

rep

rese

nt

the

amou

nt

of b

asil

Sh

eila

sh

ould

add

to

the

20%

ble

nd.

a.

Com

plet

e th

e ta

ble

repr

esen

tin

g th

e pr

oble

m.

Ou

nce

sA

mo

un

t o

f B

asil

20%

Bas

il B

len

d

100%

Bas

il

30%

Bas

il B

len

d

b

. W

rite

an

equ

atio

n t

o re

pres

ent

the

prob

lem

.

c.

How

man

y ou

nce

s of

bas

il s

hou

ld S

hei

la u

se t

o m

ake

the

30%

ble

nd?

d

. H

ow m

any

oun

ces

of t

he

20%

ble

nd

shou

ld s

he

use

?

2. H

IKIN

G A

t 7:

00 A

.M.,

two

grou

ps o

f h

iker

s be

gin

21

mil

es a

part

an

d h

ead

tow

ard

each

ot

her

. Th

e fi

rst

grou

p, h

ikin

g at

an

ave

rage

rat

e of

1.5

mil

es p

er h

our,

carr

ies

ten

ts,

slee

pin

g ba

gs, a

nd

cook

ing

equ

ipm

ent.

Th

e se

con

d gr

oup,

hik

ing

at a

n a

vera

ge r

ate

of 2

mil

es p

er h

our,

carr

ies

food

an

d w

ater

. Let

t r

epre

sen

t th

e h

ikin

g ti

me.

a.

Cop

y an

d co

mpl

ete

the

tabl

e re

pres

enti

ng

the

prob

lem

.

rt

d =

rt

Firs

t g

rou

p o

f h

iker

s

Sec

on

d g

rou

p o

f h

iker

s

b

. W

rite

an

equ

atio

n u

sin

g t

that

des

crib

es t

he

dist

ance

s tr

avel

ed.

c.

How

lon

g w

ill

it b

e u

nti

l th

e tw

o gr

oups

of

hik

ers

mee

t?

3. S

ALE

S S

ergi

o se

lls

a m

ixtu

re o

f Vir

gin

ia p

ean

uts

an

d S

pan

ish

pea

nu

ts f

or $

3.40

per

po

un

d. T

o m

ake

the

mix

ture

, he

use

s V

irgi

nia

pea

nu

ts t

hat

cos

t $3

.50

per

pou

nd

and

Spa

nis

h p

ean

uts

th

at c

ost

$3.0

0 pe

r po

un

d. H

e m

ixes

10

pou

nds

at

a ti

me.

a.

How

man

y po

un

ds o

f Vir

gin

ia p

ean

uts

doe

s S

ergi

o u

se?

b

. H

ow m

any

pou

nds

of

Spa

nis

h p

ean

uts

doe

s S

ergi

o u

se?

0.20

(16

- b

) +

1.0

0b =

0.3

0(16

)

2 o

z

14 o

z

1.5t

+ 2

t =

21

6 h

8 lb

2 lb

16 -

b0.

20(1

6 -

b)

b1.

00b

160.

30(1

6)

1.5

t1.

5t2

t2t

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5712

/22/

10

12:1

8 P

M



Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Prac

tice

Weig

hte

d A

vera

ges

2-9

Cha

pte

r 2

58

Gle

ncoe

Alg

ebra

1

1.G

RA

SS S

EED

A n

urs

ery

sell

s K

entu

cky

Blu

e G

rass

see

d fo

r $5

.75

per

pou

nd

and

Tal

l F

escu

e se

ed f

or $

4.50

per

pou

nd.

Th

e n

urs

ery

sell

s a

mix

ture

of

the

two

kin

ds o

f se

ed f

or

$5.2

5 pe

r po

un

d. L

et k

rep

rese

nt

the

amou

nt

of K

entu

cky

Blu

e G

rass

see

d th

e n

urs

ery

use

s in

5 p

oun

ds o

f th

e m

ixtu

re.

a.

Com

plet

e th

e ta

ble

repr

esen

tin

g th

e pr

oble

m.

Nu

mb

er o

f P

ou

nd

sP

rice

per

Po

un

dC

ost

Ken

tuck

y B

lue

Gra

ss

Tall

Fesc

ue

Mix

ture

b

. W

rite

an

equ

atio

n t

o re

pres

ent

the

prob

lem

.

c.

How

mu

ch K

entu

cky

Blu

e G

rass

doe

s th

e n

urs

ery

use

in

5 p

oun

ds o

f th

e m

ixtu

re?

d

. H

ow m

uch

Tal

l F

escu

e do

es t

he

nu

rser

y u

se i

n 5

pou

nds

of

the

mix

ture

?

2. T

RA

VEL

Tw

o co

mm

ute

r tr

ain

s ca

rry

pass

enge

rs b

etw

een

tw

o ci

ties

, on

e tr

avel

ing

east

, an

d th

e ot

her

wes

t, o

n d

iffe

ren

t tr

acks

. Th

eir

resp

ecti

ve s

tati

ons

are

150

mil

es a

part

. B

oth

tra

ins

leav

e at

th

e sa

me

tim

e, o

ne

trav

elin

g at

an

ave

rage

spe

ed o

f 55

mil

es p

er

hou

r an

d th

e ot

her

at

an a

vera

ge s

peed

of

65 m

iles

per

hou

r. L

et t

rep

rese

nt

the

tim

e u

nti

l th

e tr

ain

s pa

ss e

ach

oth

er.

a.

Cop

y an

d co

mpl

ete

the

tabl

e re

pres

enti

ng

the

prob

lem

.

rt

d =

rt

Firs

t Tra

in

Sec

on

d T

rain

b

. W

rite

an

equ

atio

n u

sin

g t

that

des

crib

es t

he

dist

ance

s tr

avel

ed.

c. H

ow l

ong

afte

r de

part

ing

wil

l th

e tr

ain

s pa

ss e

ach

oth

er?

3. T

RA

VEL

Tw

o tr

ain

s le

ave

Ral

eigh

at

the

sam

e ti

me,

on

e tr

avel

ing

nor

th, a

nd

the

oth

er

sou

th. T

he

firs

t tr

ain

tra

vels

at

50 m

iles

per

hou

r an

d th

e se

con

d at

60

mil

es p

er h

our.

In h

ow m

any

hou

rs w

ill

the

trai

ns

be 2

75 m

iles

apa

rt?

4. J

UIC

E A

pin

eapp

le d

rin

k co

nta

ins

15%

pin

eapp

le ju

ice.

How

mu

ch p

ure

pin

eapp

le ju

ice

shou

ld b

e ad

ded

to 8

qu

arts

of

the

pin

eapp

le d

rin

k to

obt

ain

a m

ixtu

re c

onta

inin

g 50

% p

inea

pple

juic

e?

5.75

k +

4.5

0(5

- k

) =

5.2

5(5)

3 lb

2 lb

55t

+ 6

5t =

150

1.25

h

2.5

h

5.6

qt

k$5

.75

5.75

k

5 -

k$4

.50

4.50

(5 -

k)

$5.2

55.

25(5

)5

55t

55t

65t

65t

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5812

/22/

10

12:1

8 P

M


NA

ME

DAT

E

P

ER

IOD

Lesson 2-9

Wor

d Pr

oble

m P

ract

ice

Weig

hte

d A

vera

ges

2-9

Cha

pte

r 2

59

Gle

ncoe

Alg

ebra

1

1. D

RIV

ING

Th

e dr

ive

from

New

Yor

k C

ity

to B

osto

n i

s ab

out

240

mil

es. I

t to

ok

Sam

ir 5

hou

rs t

o dr

ive

one

way

, bu

t du

e to

sev

ere

wea

ther

it

took

him

6.5

hou

rs

for

the

retu

rn t

rip.

Wh

at w

as h

is a

vera

ge

spee

d ro

un

d tr

ip?

Rou

nd

the

answ

er t

o th

e n

eare

st h

un

dred

th.

2. G

RA

DES

In

mat

h c

lass

es a

t G

orbi

ne

Hig

h S

choo

l, al

l te

sts

are

give

n d

oubl

e th

e w

eigh

t of

a q

uiz

or

hom

ewor

k sc

ore

wh

en c

alcu

lati

ng

grad

es. U

se D

onn

a’s

gr

ade

reco

rd s

hee

t to

det

erm

ine

her

av

erag

e gr

ade

so f

ar t

his

ter

m.

3. M

IXTU

RE

Kei

th w

ants

to

crea

te a

dri

nk

that

is

40%

juic

e. H

ow m

uch

of

a 10

%

juic

e so

luti

on s

hou

ld h

e ad

d to

100

m

illi

lite

rs o

f 10

0% g

rape

juic

e to

obt

ain

th

e 40

% m

ixtu

re?

4. B

USI

NES

S M

rs. W

insh

ip s

ells

ch

ocol

ate

fudg

e fo

r $7

.50

per

pou

nd

and

pean

ut

butt

er f

udg

e fo

r $7

.00

per

pou

nd.

Th

e to

tal

nu

mbe

r of

pou

nds

sol

d on

Sat

urd

ay

was

146

an

d th

e to

tal

amou

nt

of m

oney

co

llec

ted

was

$10

65. H

ow m

any

pou

nds

of

eac

h t

ype

of f

udg

e w

ere

sold

?

5. T

RA

INS

Tw

o tr

ain

s ar

e 50

00 f

eet

apar

t,

hea

din

g to

war

d ea

ch o

ther

, bu

t on

se

para

te p

aral

lel

stra

igh

t tr

acks

, Tra

in A

is

tra

veli

ng

at 4

5 m

iles

per

hou

r an

d T

rain

B i

s tr

avel

ing

at 2

4 m

iles

per

hou

r.

a.

Ch

ange

45

mil

es p

er h

our

and

24

mil

es p

er h

our

into

fee

t pe

r se

con

d.

b

. A

bou

t h

ow f

ar w

ill

each

tra

in t

rave

l be

fore

th

ey m

eet?

Rou

nd

you

r an

swer

s to

th

e n

eare

st h

un

dred

th.

c. In

how

man

y se

con

ds w

ill T

rain

A a

nd

Tra

in B

mee

t?

A

ssig

nm

ent

Gra

de

H

omew

ork

chap

ter

1 95

Q

uiz

chap

ter

1 80

Te

st c

hapt

er 1

92

H

omew

ork

chap

ter

2 93

Q

uiz

chap

ter

2 96

Te

st c

hapt

er 2

81

4

1.74

mile

s p

er h

ou

r

8

8.75

2

00

mL

8

6 p

ou

nd

s o

f ch

oco

late

an

d 6

0 p

ou

nd

s o

f p

ean

ut

butt

er

Trai

n A

: 66

fee

t p

er s

eco

nd

Tr

ain

B:

35.2

fee

t p

er s

eco

nd

Trai

n A

: 32

60.8

7 fe

etTr

ain

B:

1739

.13

feet

49.4

sec

on

ds

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

5912

/22/

10

12:1

8 P

M



An

swer

s

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Enri

chm

ent

2-9

Cha

pte

r 2

60

Gle

ncoe

Alg

ebra

1

Exp

ecte

d V

alu

eE

xpec

ted

valu

e is

th

e av

erag

e re

turn

of

an e

ven

t ov

er r

epea

ted

tria

l. E

xpec

ted

valu

e is

als

o a

form

of

wei

ghte

d av

erag

e an

d ca

n b

e u

sed

to d

eter

min

e w

het

her

or

not

you

sh

ould

pla

y a

gam

e ba

sed

on w

hat

th

e ex

pect

ed v

alu

e of

you

r w

inn

ings

is.

It

can

als

o be

use

d to

det

erm

ine

the

expe

cted

len

gth

of

a ga

me.

Y

ou a

re r

olli

ng

a d

ie t

o d

eter

min

e th

e n

um

ber

of

can

dy

bar

s yo

u

wil

l w

in a

t a

sch

ool

fair

. If

you

rol

l a

one,

you

get

12

can

dy

bar

s. I

f yo

u r

oll

a tw

o or

a t

hre

e, y

ou g

et 3

can

dy

bar

s. I

f yo

u r

oll

a fo

ur,

fiv

e or

six

, you

get

2

can

dy

bar

s.

Sin

ce t

her

e ar

e si

x po

ssib

ilit

ies

for

wh

at y

ou c

an r

oll:

•

1 −

6 o

f th

e ti

me,

you

wil

l w

in 1

2 ca

ndy

bar

s.

•

2 −

6 o

r 1 −

3 o

f th

e ti

me,

you

wil

l w

in 3

can

dy b

ars.

•

3 −

6 o

r 1 −

2 o

f th

e ti

me,

you

wil

l w

in 2

can

dy b

ars.

Th

e ex

pect

ed v

alu

e is

1 −

6 (1

2) +

1 −

3 (3

) +

1 −

2 (2

) or

4 c

andy

bar

s.

Th

eref

ore,

if

you

pla

yed

the

gam

e 10

0 ti

mes

, you

cou

ld e

xpec

t to

win

abo

ut

4 ca

ndy

bar

s ea

ch t

ime.

Exer

cise

sF

ind

th

e ex

pec

ted

val

ue

of e

ach

of

the

foll

owin

g ev

ents

.

1. Y

ou a

re f

lipp

ing

a co

in. I

f yo

u f

lip

hea

ds, y

ou w

in $

5.00

. If

you

fli

p ta

ils,

you

win

$1.

00.

2. Y

ou a

re r

olli

ng

a di

e to

det

erm

ine

the

nu

mbe

r of

can

dy b

ars

you

wil

l w

in a

t a

sch

ool

fair

. If

you

rol

l a

1, y

ou g

et 1

8 ca

ndy

bar

s. I

f yo

u r

oll

a 2

or a

3, y

ou g

et 6

can

dy b

ars.

If

you

ro

ll a

4, 5

or

6, y

ou g

et 0

can

dy b

ars.

3. Y

ou a

re r

olli

ng

a di

e to

det

erm

ine

the

amou

nt

of m

oney

you

wil

l w

in a

t a

sch

ool

fair

. If

you

rol

l a

1, y

ou g

et $

12.0

0.

If y

ou r

oll

a 2

or a

3, y

ou g

et $

3.00

. If

you

rol

l a

4, 5

or

6,

you

ow

e $2

.00.

4. Y

ou a

re f

lipp

ing

a co

in. I

f yo

u f

lip

hea

ds, y

ou w

in $

10. I

f yo

u f

lip

tail

s, y

ou w

in $

2.

5. Y

ou a

re r

olli

ng

a di

e to

det

erm

ine

the

nu

mbe

r of

can

dy b

ars

you

wil

l w

in a

t a

sch

ool

fair

. If

you

rol

l a

1, y

ou g

et 2

4 ca

ndy

bar

s.

If y

ou r

oll

a 2

or a

3, y

ou g

et 6

can

dy b

ars.

If

you

ro

ll a

4, 5

or

6, y

ou g

et n

one.

Exam

ple

$3.0

0

5 $2.0

0

$6.0

0

6

042_

060_

ALG

1_A

_CR

M_C

02_C

R_6

6131

5.in

dd

6012

/22/

10

12:1

8 P

M



Chapter 2 Assessment Answer Key Quiz 1 (Lessons 2-1 through 2-3) Quiz 3 (Lessons 2-6 and 2-7) Mid Chapter TestPage 63 Page 64 Page 65

Quiz 2 (Lessons 2-4 and 2-5)

Page 63 Quiz 4 (Lessons 2-8 and 2-9) Page 64

Part I

Part II

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

y 2 - 12 = 5x

Two times b minus 10 equals 4.

The sum of y and the product of 3 and the square of x is 5 times x.

14

-49

-9

40

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

7

84

-5

no solution

0

7

C

D

11

5

-5

{2, 5}

{-6, 7}

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. B

$19.08

increase; 25%

decrease; 28%

99

27

15

no

no

yes

1.

2.

3.

4.

5.

6. G

H

A

J

7.

8.

9.

10.

11.

12. {-2, 5}

Four times n equals x times the difference of fi ve and n.

$116.15

-2

B

0

all numbers

B

-3 -2 -1 0 1 2 3 4 5

1.

2.

3.

4.

5. ℓ =

p - 2w

_ 2 ; 14 m

A

4 g

b = x - ac

x = p + r

_

n


Chapter 2 Assessment Answer KeyVocabulary Test Form 1Page 66 Page 67 Page 68

B

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass


1.

2.

3.

4.

5.

6.

7.

ratio

weighted average

percent of change

rate

multi-step equation

unit rate

identity

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

F

C

D

J

A

G

B

D

H

G

F

B

J

B

H

C

J

A

H

B 11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 45

8.

9.

Sample answer: A proportion is an equation stating that two ratios are equal.

Sample answer: A formula is an equation that states a rule for the relationship between certain quantities.


Chapter 2 Assessment Answer KeyForm 2A Form 2BPage 69 Page 70 Page 71 Page 72

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10. G

G

C

F

D

H

A

J

C

C

11.

12.

13.

14.

15.

16.

17.

18.

19.

20. H

B

F

D

G

C

G

C

F

B

B: 4 L

11.

12.

13.

14.

15.

16.

17.

18.

19.

20. H

A

F

B

J

B

F

C

J

B

B: 21

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. G

B

J

A

J

A

H

C

H

B


Chapter 2 Assessment Answer KeyForm 2CPage 73 Page 74

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass


15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 8

2.5 h

3 L

$12.84

22.5

yes

-1

all numbers

13

x = bc

_ a

decrease; 20%

h = V

_ πr2

; 10.5 in.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

$134.40

5n + 12 = -3; -3

n - 3.5 = 12.7; 16.2

Three times the sum of x and y equals two

times y minus x.

36 - x = 3(4 + x)

6

45

14 2 _ 5

5

-5

-9

3

{

-1, 7 _ 5 }

{-1, 0}-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4


Chapter 2 Assessment Answer KeyForm 2DPage 75 Page 76

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: $9.60

4 h

7.5 lb of nuts, 2.5 lb of dried fruit

$13.50

increase; 25%

r = n(4v - t)

11

no solution

3

20

no

h = V

_ πr2

; 18.67 in.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

$176.80

n - 8.1 = 4.9; 13

7

50

7 5

_ 7

7

4

Three divided by y minus

fi ve equals x times the

sum of y and 7.

18 + n = 7(n - 3)

6n + 15 = 9; -1

11

{-3, -1}

{-4, -2}

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1 2 3 4

7


Chapter 2 Assessment Answer KeyForm 3Page 77 Page 78

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15. 10 ft

yes

10

Five times the sum of two times

x and three times y equals the

square of y minus two times the

cube of x.

(x + 2)10

= 8x + 36; 8

3 _ 5 x

= 1; 5 _

3

8

126

-1 2 _ 13

-2 2 _ 3

-13

-27

{-7, -5}

$4000

-8 -7 -6 -4 -3 -2 -1-5 0

x - 45 _

12 + 20 = 5(32 + x)

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: 12 mi

1.95 ft/s

510 mph, 540 mph

$7000

$63.60

increase; 12%

x = ry - t

_ 4

x = r + n _

a

2

- 7 _ 9

- 6


Chapter 2 Assessment Answer Key

Page 79, Extended-Response Test Scoring Rubric

Score General Description Specifi c Criteria

4 SuperiorA correct solution that is supported by well-developed, accurate explanations

• Shows thorough understanding of the concepts of translating between verbal sentences and equations, solving equations, percents of increase and decrease, uniform motion problems, and proportions.

• Uses appropriate strategies to solve problems. • Computations are correct. • Written explanations are exemplary. • Goes beyond requirements of some or all problems.

3 Satisfactory A generally correct solution, but may contain minor fl aws in reasoning or computation

• Shows an understanding of the concepts of translating between verbal sentences and equations, solving equations, percents of increase and decrease, uniform motion problems, and proportions.

• Uses appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are effective.

• Satisfi es all requirements of problems.

2 Nearly SatisfactoryA partially correct interpretation and/or solution to the problem

• Shows an understanding of most of the concepts of translating between verbal sentences and equations, solving equations, percents of increase and decrease, uniform motion problems, and proportions.

• May not use appropriate strategies to solve problems.

• Computations are mostly correct.

• Written explanations are satisfactory.

• Satisfi es the requirements of most of the problems.

1 Nearly Unsatisfactory A correct solution with no supporting evidence or explanation

• Final computation is correct. • No written explanations or work is shown to substantiate the

fi nal computation. • Satisfi es minimal requirements of some of the problems.

0 UnsatisfactoryAn incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given

• Shows little or no understanding of most of the concepts of translating between verbal sentences and equations, solving equations, percents of increase and decrease, uniform motion problems, and proportions.

• Does not use appropriate strategies to solve problems. • Computations are incorrect. • Written explanations are unsatisfactory. • Does not satisfy requirements of problems. • No answer may be given.

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



Chapter 2 Assessment Answer Key Page 79, Extended-Response Test Sample Answers

1a. The student should explain that the first phrase is a product of x and y and then the addition of z, while the second phrase is a product of x and the quantity y + z.

1b. Check that the student’s values for x, y, and z satisfy both xy + z and x(y + z). One example is x = 1, y = 2, and z = 3. Another example is x = 2, y = 3, and z = 0.

2a. ry + z

_ m - t = x

(Original equation)

ry + z

_ m - t + t = x + t

(Add t to each side.)

ry + z

_ m = x + t

(Simplify.)

m ( ry + z

_ m ) = m(x + t)

(Multiply each side by m.)

ry + z = mx + mt (Simplify.)

ry + z - z = mx + mt - z (Subtract z from each side.)

ry = mx + mt - z (Simplify.)

ry

_ r = mx + mt - z _ r

(Divide each side by r.)

y = mx + mt - z _ r

(Simplify.)

The value of y is mx + mt - z __ r

2b. Division by 0 is undefined, so in the original equation m ≠ 0, and in the final equation r ≠ 0.

3a. The student should conclude that a 10% decrease followed by a 10% increase results in a net decrease of 1%. Thus, the final cost would be 99% of the original price.

3b. Since multiplication is commutative, multiplying by 1.1 and then 0.9 would yield the same result as multiplying by 0.9 and then 1.1. The student should conclude that a 10% increase followed by a 10% decrease yields the same result as a 10% decrease followed by a 10% increase.

4a. Since the two people walked for the same amount of time and time can be calculated as distance divided by rate, the proportion

Tony’s distance __

Tony’s rate =

can be used to solve this problem.

4b. The length of Tony’s walk can be calculated directly from his rate of 3 miles per hour and his distance of 6 miles. Ivia walked 1 mile per hour faster, so her rate is 4 miles per hour. The length of Ivia’s walk can be calculated directly from her rate of 4 miles per hour and distance of 6 miles. Thus, a proportion would not be used to solve this problem.

5a. Sample answer: x + 2 = 10, x - 2 = 6, 2x = 16, x _

2 = 4

5b. Sample answer: 2x + 1 = x + 9

5c. These two equations are equivalent. The solution to both equations is 5. The student should recognize that the solution to all equations in parts a and b is 8. Therefore neither of these two equations could be equivalent to any of the equations created for parts a and b.

In addition to the scoring rubric found on page A40, the following sample answers may be used as guidance in evaluating extended-response assessment items.

Ivia’s distance __ Ivia’s rate

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass



Chapter 2 Assessment Answer KeyStandardized Test Practice

Page 80 Page 81

15.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

1

16.

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

9

8

7

6

5

4

3

2

1

0

42

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9. A B C D

F G H J

A B C D

F G H J

A B C D

F G H J

A B C D

A B C D

F G H J

10.

11.

12.

13.

14. F G H J

A B C D

F G H J

A B C D

F G H J


Chapter 2 Assessment Answer KeyStandardized Test PracticePage 82

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass


17.

18.

19. Sample answer:

20.

21.

22.

23.

24.

25.

26.

27a.

27b.

7 L

m = x(t - p)

3

-3

7

31

85 - 9y = 7(4 + y)

5u + 9x

22

No; since multiplication

is commutative, a 10%

increase followed by a

10% decrease would

have the same result as

a 10% decrease followed

by a 10% increase.

y

xO

The fi nal price would

be 99% of the

original price.


Chapter 2 Assessment Answer KeyUnit 1 TestPage 83 Page 84

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

Sample answer: the

difference of m squared

and 4 is equal to the

sum of 2 times r plus 1

6x + 12

Time

Tem

per

atu

re (

°F)

False

23a + 6b

7r + 9t

7t2 + 3t

Multiplicative Inverse

Property; 1 _ 6

{4}

71

5 - n 3

Sample answer: Four

math textbooks are

stacked on top of two

science textbooks. Write

an expression for the total

height of the stack of

books.

yes

no

8

Sample answer: the sum

of four times r and 9

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30. 8 lb

v = t - kr

$3.91

3 2 _ 7

11

-2

56

42

-12

-18

1

all real numbers

yes-2-3 -1 0 1 2 4 5 6 7 83

{-2, 3}


Chapter 2 Resource Masters - Commack Schools

Documents

Transcript of Chapter 2 Resource Masters - Commack Schools