Coming Up:Today: • Review Quiz 2 • Lecture on Section 2.4: Word problems!• NOTE: This homework is due at the beginning of the next

class session.

Coming up at the next three class sessions:1. Lecture on Section 2.52. Review for Test 13. Test 1 on Mon. November 9th (MW) or Thursday November 12th (T/Th) Test 1 on all sections covered this semester up to this point (including material covered on Quizzes 1 and 2, plus sections 2.4 and 2.5)

Gateway Quiz Retake Facts

• MUST pass with 100% to pass Math 010• So far: Two attempts to pass in class– If not passed during one of those two attempts:• One attempt per week for rest of semester

– Seven weeks = seven chances to pass

• Outside of class time: scheduled times will be given today and posted on bulletin boards.

Math TLC Open Lab open M-Th 8:00 am to 7:30 pmJarvis Hall Science Wing 203

Didn’t pass your Gateway Quiz?Here are the next steps:• Go over the incorrect answers on your previous

attempts with a TA (and get their signature) in the Math TLC Open Lab (JHSW 203).

• Take another Practice Gateway Quiz.– Go over any incorrect answers on the practice

attempts with a TA in the Math TLC Open Lab• Have a TA in the Math TLC Open Lab sign you

up for a retake time

• Wednesdays– 10:10 am– 11:15 am

• Thursdays– 10:10 am– 11:15 pm

Gateway Quiz Retake Times(One new attempt allowed per week, beginning November 2)

SIGN UP IN THE MATH TLC OPEN LAB!If NONE of the above times work for you…

email Krystle Mayer, Math TLC Coordinator (JHSW 201), to set up a date and time.

• Mondays– 1:25 pm– 2:30 pm

• Tuesdays– 1:25 pm– 3:35 pm

Grade Scale

Online Quiz 2 Results:• Average class score after partial credit: XX.X%

• Commonly missed questions: # _________________

• If you got less than 70% on Quiz 2, make sure to go over your quiz with me or a TA sometime today or tomorrow to help you prepare for the upcoming midterm test.

Grade A A- B+ B B- C+ C C- F

Points ≥ 925 ≥ 900 ≥ 875 ≥ 825 ≥ 800 ≥ 775 ≥ 725 ≥ 700 < 700

% Score ≥ 92.5 ≥ 90 ≥ 87.5 ≥ 82.5 ≥ 80 ≥ 77.5 ≥ 72.5 ≥70 < 70

Please

CLOSE

YOUR LAPTOPS,and turn off and put away your

cell phones,

and get out your note-taking materials.

Section 2.4: Application Problems:

General strategy for problem solving:1) Understand the problem• Read and reread the problem• Choose a variable to represent the unknown• Construct a drawing, whenever possible

2) Translate the problem into an equation

3) Solve the equation

4) Interpret the result• Check solution• State your conclusion

Example 1:

The product of twice a number and three is the same as the difference of five times the number and ¾. Find the number.

Understand - Read and reread the problem.

- Choose a variable to represent your unknown.

If we let x = the unknown number, then

“twice a number” translates to 2x,

“the product of twice a number and three” translates to 2x · 3,

“five times the number” translates to 5x, and

“the difference of five times the number and ¾” translates to 5x - ¾ .

Example (cont.)

Translate

The product of

·

twice a number

2x

and 3

3

is the same as

=

5 times the number

5x

and ¾

¾

the difference of

–

Example (cont.)

Solve

2x · 3 = 5x – ¾

6x = 5x – ¾ (simplify left side)

6x + (-5x) = 5x + (-5x) – ¾ (add –5x to both sides)

x = - ¾ (simplify both sides)

Now CHECK your answer (see if both sides produce the same answer when you put -3/4 in place of x):

Left side: 2x·3= (2·-3/4)·3 = -6/4 · 3 = -3/2 · 3= -9/2

Right side: 5x – 3/4 = 5·3/4 – 3/4 = -15/4 – 3/4 = -18/4 = -9/2

And this problem:

Twice the product of a number and three is the same as five times the difference of the number and ¾. Find the number.

Consider the difference between the last problem:

The product of twice a number and three is the same as the difference of five times the number and ¾. Find the number.

(Answer = -3/4)Equation: 2x · 3 = 5x – ¾

Equation: 2(x · 3) = 5(x – ¾) (Answer = -15/4)

Sample homework problem:

Answer: -6

How would you set this problem up?

5(x – 4) = 4 + 5x + 4x

Example

A car rental agency advertised renting a Toyota Prius for $25 per day and $0.20 per mile. If you rent this car for 2 days, how many miles can you drive on a $100 budget?

Understand Read and reread the problem.

Just to get an idea of what’s going on in this problems, let’s start by considering what the cost would be if we were to drive a total of 100 miles over the 2 days.

In this case our equation for the total cost would come from taking

twice the daily rate and adding the fee for mileage to get

2(25) + 0.20(100) = 50.00 + 20 = $70.00.

This gives us an idea of how the cost is calculated, and we also now know that if we have $100 to spend, we can drive more than 100 miles.

Example (cont.)

Translate

Daily costs

2(25)

mileage costs

0.20x

plus

+

is equal to

= 100

maximum budget

So to generalize this specific example of 100 miles, if we let x = the number of miles driven, then 0.29x = the cost for mileage driven.

To do this problem without a calculator, we will want to convert the decimal 0.20 into the fraction 20/100.

Example (cont.)

Solve

2(25) + 20/100 x = 100

50 + 20/100 x = 100 (simplify left side)

20/100 x = 50 (simplify both sides)

50 – 50 + 20/100 x = 100 – 50 (subtract 50 from both sides)

2050

100

100 100

20 20x (multiply both sides by 100/20)

x = 50∙5 = 250 (simplify both sides)

Example (cont.)

Interpret

Check: If we replace “number of miles” in the problem with 250, then 50 + 0.20(250) = 50 + 50, which is equal to our budget of $100.

State your answer: The maximum number of miles we can drive is 250.

Answer: First piece is 4 inches, second is 12, third is 20.

Hint: Start by drawing a picture.

Example:

The sum of three consecutive integers is 366. What are the three integers?

Solution:• Call the first integer x. • Then what is the next consecutive integer?

• x + 1• And the third one?

• x + 2• So the sum would be what?

• x + x + 1 + x + 2• This simplifies to 3x + 3

• And the equation would be what?• 3x + 3 = 366

Example (cont):The sum of three consecutive integers is 366. What are the three integers?

Solution (cont):• Now solve the equation

• 3x + 3 = 366• 3x = 363• x = 363/3 = 121

• Now answer the question:• First integer = x

• x = 121• Second integer = x + 1

• = 122• Third integer = x + 2

• = 123

Example (cont):The sum of three consecutive integers is 366. What are the three integers?

Now check your solution: (121, 122, 123)

• Are these three numbers integers?• Yes

• Are they consecutive?• Yes

• Do they add up to 366?• 121 + 122 + 123 = 243 + 123 = 366• Yes

Example:

The sum of three consecutive even integers is 366. What are the three integers?

Solution:• Call the first integer x. • Then what is the next consecutive even integer?

• x + 2• And the third one?

• x + 4• So the sum would be what?

• x + x + 2 + x + 4• This simplifies to 3x + 6

• And the equation would be what?• 3x + 6 = 366

Now let’s change the problem slightly:

Example (cont):The sum of three consecutive even integers is 366. What are the three integers?

Solution (cont):• Now solve the equation

• 3x + 6 = 366• 3x = 360• x = 360/3 = 120

• Now answer the question:• First integer = x

• x = 120• Second integer = x + 2

• = 122• Third integer = x + 4

• = 124

Example (cont):The sum of three consecutive integers is 366. What are the three integers?

Now check your solution: (120, 122, 124)

• Are these three numbers integers?• Yes

• Are they even?• Yes

• Do they add up to 366?• 120 + 122 + 124 = 242 + 124 = 366• Yes

Reminder:This homework on Section 2.4 is due at start of next class session.

You may want to come in to the lab for help on this homework. Many students find that these problems take a bit longer to figure out than previous assignments.

Also, please remember to come in to the lab for your Gateway quiz review and get your worksheet signed, then sign up with a TA in the open lab for one of the time slots for this week’s retake.

• Wednesdays– 10:10 am– 11:15 am

• Thursdays– 10:10 am– 11:15 pm

Gateway Quiz Retake Times(One new attempt allowed per week, beginning November 2)

SIGN UP IN THE MATH TLC OPEN LAB!If NONE of the above times work for you…

email Krystle Mayer, Math TLC Coordinator (JHSW 201), to set up a date and time.

• Mondays– 1:25 pm– 2:30 pm

• Tuesdays– 1:25 pm– 3:35 pm

Note to instructors: The remaining slides contain additional problems from today’s homework that you might want to cover if time allows.

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework:

Problem from today’s homework: