Course 1

7-9 Percent Problems7-9 Percent Problems

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

7-9 Percent Problems

Warm UpWrite each decimal as a percent and fraction.

1. 0.38

2. 0.06

3. 0.2

38%,

6%,

20%,

1950

__

350

__

1 5

__

Course 1

7-9 Percent Problems

Problem of the Day

Lucky Jim won $16,000,000 in a lottery. Every year for 10 years he spent 50% of what was left. How much did Lucky Jim have after 10 years?

$15,625

Course 1

7-9 Percent Problems

Learn to find the missing value in a percent problem.

Course 1

7-9 Percent Problems

To find the percent one number is of another, use this proportion:

% 100

= is of

If you are looking for 45% of 420, 45 replaces the percent sign and 420 replaces “of.” The first denominator, 100, always stays the same. The “is” part is what you have been asked to find.

Course 1

7-9 Percent Problems

Additional Example 1: Application

First estimate your answer. Think: 35% = ,

which is close to , and 560 is close to 600. So

about of the students participate in after-school sports.

35100

___

1 3

__

1 3

__

1 3

__ This is the estimate.• 600 = 200

Think: “35 out of 100 is how many out of 560?”

Helpful Hint

There are 560 students in Ella’s school. If 35% of the students participate in after-school sports, how many students participate in after-school sports?

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7-9 Percent Problems

Additional Example 1 ContinuedNow solve:

s 560

___ 35 100

___ =

100 • s = 35 • 560

100s = 19,600

100s 100

____ 19,600 100

_____ =

s = 196

Let s represent the number of students who participate in after-school sports.

The cross products are equal.

s is multiplied by 100.

Divide both sides of the equation by 100 to undo multiplication.

Since 196 is close to your estimate of 200, 196 is a reasonable answer.

196 students participate in after-school sports.

Course 1

7-9 Percent Problems

Check It Out: Example 1

There are 480 students in Tisha’s school. If 70% of the students participate in the fundraising program, how many students participate in the fundraising program?

First estimate your answer. Think: 70% = ,

which is close to , and 480 is close to 500. So

about of the students participate in after

school sports.

70100

___

3 4

__

3 4

__

This is the estimate. 3 4

__ • 500 = 375

Course 1

7-9 Percent Problems

Check It Out: Example 1 ContinuedNow solve:

s 480

___ 70 100

___ =

100 • s = 70 • 480

100s = 33,600

100s 100

____ 33,600 100

_____ =

s = 336

Let s represent the number of students who participate in the fundraising program.

The cross products are equal.

s is multiplied by 100.

Divide both sides of the equation by 100 to undo multiplication.

Since 336 is close to your estimate of 375, 336 is a reasonable answer.

336 students participate in the fundraising program.

Course 1

7-9 Percent Problems

Additional Example 2: Application

Johan is 25% of the way through his exercises. If he has exercised for 20 minutes so far, how much longer does he have to work out?

is of

__ % 100

___ =

100 • 20 = 25 • m

25% of the exercises are completed, so 20 minutes is 25% of the total time needed.

The cross products are equal.

20 m

__ 25 100

___ = Set up a proportion. The “of” part is what you have been asked to find.

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7-9 Percent Problems

Additional Example 2 Continued

2,000 = 25m

2,000 25

_____ 25m 25

____ =

80 = m

m is multiplied by 25.

Divide both sides by 25 to undo multiplication.

The time needed for the exercises is 80 min. So far, the exercises have taken 20 min. Because 80 – 20 = 60, Johan will be finished in 60 min.

Course 1

7-9 Percent Problems

Check It Out: Example 2

Phil is 30% of the way through his homework. If he has worked for 15 minutes so far, how much longer does he have to work?

is of

__ % 100

___ =

100 • 15 = 30 • m

30% of the exercises are completed, so 15 minutes is 30% of the total time needed.

The cross products are equal.

15 m

__ 30 100

___ = Set up a proportion. The “of” part is what you have been asked to find.

Course 1

7-9 Percent Problems

Check It Out: Example 2 Continued

1,500 = 30m

1,500 30

_____ 30m 30

____ =

50 = m

m is multiplied by 30.

Divide both sides by 30 to undo multiplication.

The time needed for the homework is 50 min. So far, the homework has taken 15 min. Because 50 – 15 = 35, Phil will be finished in 35 min.

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7-9 Percent Problems

Instead of using proportions, you can also multiply to find a percent of a number.

Course 1

7-9 Percent Problems

Additional Example 3: Multiplying to Find a Percent of a Number

36% = 0.36

0.36 • 50

Write the percent as a decimal.

Multiply using the decimal.

18So 18 is 36% of 50.

Find 36% of 50.

0 5 10 15 20 25 30 35 40 45 50

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

CheckUse a model to check the answer.

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7-9 Percent Problems

Check It Out: Example 3

20% = 0.20

0.20 • 70

Write the percent as a decimal.

Multiply using the decimal.

14So 14 is 20% of 70.

Find 20% of 70.

0 7 14 21 28 35 42 49 56 63 70

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

CheckUse a model to check the answer.

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7-9 Percent Problems

Lesson Quiz

1. Find 28% of 310.

2. Find 70% of 542.

3. Martha is taking a 100-question test. She has completed 60% of the test in 45 minutes. How much longer will it take her to finish the test?

4. Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies does she have?

379.4

86.8

30 min

18