Warm Up Sept. 12th Sit in your usual seat with your tracking sheet out and your

homework on your desk. Answer the following questions on your OWN sheet of paper.

1. Solve for h: 8(h – 1) = 6h + 4 + 2h

2. There are three consecutive integers whose sum is 39. What are the integers?

3. Membership for the Alpine rock-climbing gym costs $25 per month plus a $125 sign-up fee. Membership for Rocco’s rock-climbing gym costs $30 per month plus a $50 sign-up fee.

a) After how many months will the memberships costs the same?b) If you only wanted a one-year membership, which gym would you

join?

Homework Questions?

Finishing Variables on Both Sides…

• Instead of working with fractions, multiply the entire equation (EVERYTHING!) by the least common denominator (LCD).

1. 231

21 yy 10

23

41

x

Special Cases• In some equations, the variables cancel out. If this

happens while solving, the resulting equation determines the answer.

• Examples:1. 2(3w – 7) = 7w + 9 – w

Special Cases (cont.)2. -5(2j – 3) + j = 3(2 – 3j) + 9

Working with Ratios and Proportions!

Vocabulary• A ratio compares 2 numbers by division.

Proportions• A proportion is an equation that states that 2

ratios are equal.• Examples:1. 2.

1287 k

w8

43

You try!• Try numbers 13 and 14 on your homework

sheet.

Proportions (cont.)3. 4.

43

58

ff

65

123

j

Want some practice?• Complete problem 19 and 20 on your

homework sheet!

Applications1. An MP3 player that has 2 gigabytes of storage

can hold about 500 songs. A similar but larger MP3 has 25 gigabytes of storage. How many songs can the larger MP3 player hold?

Applications2. Josh finished 24 math problems in one hour.

At this rate, how many hours will it take him to complete 60 problems?

You try!• Work on problems 21 and 22 from your

homework sheet.

Indirect Measurement 1. A girl stands 5 feet tall and casts a shadow

that is 2 feet long. An apartment building casts a shadow that is 35 feet long. How tall is the building?

Can you do this one?2. On a map, the distance from Jacksonville to

Orlando, FL is 1.25 inches. The map has a scale factor of 1 inch = 110 miles. What is the actual distance from Jacksonville to Orlando?

Similar Figures• Similar figures have the same shape but not

necessarily the same size.• We use proportions to find missing lengths of

similar figures.1. In the diagram, ΔABC ~ ΔDEF. What is DE?

B E

A C D F

10 16 12

18

You try this one!1. In the diagram, ΔABC ~ ΔDEF. What is AC?

B E

A C D F

8 10 15

27

Vocabulary• A ratio that compares quantities measured

in different units is called a rate.

• A rate with a denominator of 1 is called a unit rate.

Comparing Unit Rates• Think about this and discuss with your

neighbor…• You are shopping for T-shirts. Which store offers

the best deal? Why?• Store A: $25 for 2 shirts• Store B: $45 for 4 shirts• Store C: $30 for 3 shirts

Converting Units• To convert from one unit to another, such as feet to

inches, multiply by a conversion factor to produce the desired units.

• A conversion factor is a ratio of 2 equivalent measures in different units.

• In other words, we set up a proportion with two equivalent ratios to find our missing unit!

Convert the following:1. 330 min. hours 2. 5 ft. 3 in. in.

Let’s practice!• Try problems 1 – 3 on your homework

sheet.

Converting Rates• A student ran 150 feet in 5.8 seconds. At what

speed did the student run in miles per minute? (1 mile = 5280 feet; 1 minute = 60 seconds)

Let’s practice!• Try problems 9 – 11 on your homework

sheet.

Homework• Working with Ratios Worksheet (all

problems we did not complete in class)