Course 3 6-3 Finding Percents 6-3 Finding Percents Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course 3

6-3 Finding Percents6-3 Finding Percents

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

6-3 Finding Percents

Warm UpRewrite each value as indicated.

1. as a percent

2. 25% as a fraction

3. as a decimal

4. 0.16 as a fraction

48%

0.375

425

24 50

3 8

14

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Problem of the Day

A number between 1 and 10 is halved, and the result is squared. This gives an answer that is double the original number. What is the starting number?8

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Learn to find percents.

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What percent of 92 is 66?

Additional Example 1A: Finding the Percent One Number Is of Another

Think: What number is to 100 as 66 is to 92?

=number

100 partwhole

Set up a proportion.

Substitute. n

100 6692

=

n 92 = 100 66

92n = 6600

Find the cross products.

Method 1: Set up a proportion to find the percent.

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Additional Example 1A Continued

n ≈ 72

= 72

100 66 92

The proportion is reasonable.

Solve for n. 92 6600n =

66 is approximately 72% of 92.

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Additional Example 1B: Finding the Percent One Number Is of Another


Method 2: Set up an equation to find the percent.

p 220 = 88 Set up an equation.

Divide both sides by 220.

p = 0.4 0.4 is 40%.

So 88 is 40% of 220.

220p220

= 88 220

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Additional Example 1B Continued

Check

88 = 88 40% of 220 is 88.

40% 220 = 88 Substitute 40% for p.?

0.40 220 = 88 Write a decimal and multiply.?

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Think: What number is to 100 as 21 is to 140?

=number

100 partwhole Set up a proportion.

Substitute. n

100 21140

=

n 140 = 100 21

140n = 2100

Find the cross products.

Check It Out: Example 1A

Method 1: Set up a proportion to find the percent.

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n = 15

The proportion is reasonable.

Solve for n.140 2100n =

21 is 15% of 140.

= 15

100 21140

Check It Out: Example 1A Continued

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Check It Out: Example 1B


Method 2: Set up an equation to find the percent.

p 110 = 11 Set up an equation.

11110

p = Solve for p.

p = 0.1 0.1 is 10%.

So 11 is 10% of 110.

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Check

11 = 11 10% of 110 is 11.

10% 110 = 11 Substitute 10% for p.?

.10 110 = 11 Write a decimal and multiply?

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Additional Example 2A: Recreation Application

First, find what percent of the grass Aimee and Ken cut.

= 20% and 0.31 = 31%.1 5

Four friends volunteered to cut the grass around their neighbor’s house. Jay cut 23%

of the grass, Aimee cut of the grass, Ken cut 0.31 of the grass, and Bryn cut the rest. What percent of the grass did Bryn cut?

1 5

Next, subtract the percents you know from 100% to find the remaining percent.

100% - 23% - 20% - 31% = 26%.

Bryn cut 26% of the grass.

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Additional Example 2B: Recreation Application

First, find what percent of his films are dramas and action.

= 40% and 0.325 = 32.5%2 5

Jeremy organizes his movie collection by genre. of his collection are dramas, 0.325 are action

films, 3% are documentaries, 19.5% are comedies, and the rest of his movies are independent films. What percent of his movie collection are independent films?

2 5


100% 40% 32.5% 3% 19.5% = 5%.5% of Jeremy’s movie collection are independent films.

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First, find what percent of the shelves Lauren and Ling stocked.

= 60% and 0.19 = 19%.3 5

Four store employees stock the shelves at the Electronics Store. Francisco stocked 14% of the shelves, Lauren stocked of the shelves, Ling stocked 0.19 of the shelves, and Mark stocked the rest. What percent of the shelves did Mark stock?

3 5


100% - 14% - 60% - 19% = 7%.

Mark stocked 7% of the shelves.

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First, find what percent of his CDs are rock and pop.

= 50% and 0.125 = 12.5%1 2

Joe organizes his CD collection by genre.

of his collection is rock, 0.125 is pop, 6% is

classical, 9.5% is country, and the rest of his CDs are jazz. What percent of his CD collection is jazz?

1 2


100% 50% 12.5% 6% 9.5% = 22%.

22% of Joe’s CD collection is jazz.

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Additional Example 3A: Finding the Percent of a Number

The city of Dallas, Texas has a population of approximately 1,189,000 people. The population of the city of Austin, Texas is 55% of the population of Dallas. To the nearest thousand, what is the population of Austin?

Choose a method: Set up a proportion.

= 55

100 p

1,189,000 Set up a proportion.

55 1,189,000 = 100 p Find the cross products.

Think: 55 is to 100 as what population is to 1,189,000.

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Additional Example 3A Continued

Austin has a population of approximately 654,000.

65,395,000 = 100p Simplify.

= 65,395,000 100

100 100


653,950 = p Simplify.

654,000 ≈ p Round to the nearest whole number.

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When solving a problem with a percent greater than 100, look for the number that will be greater than the number given.

Helpful Hint

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Additional Example 3B: Finding the Percent of a Number

After a drought, a reservoir had only 66 % of the average amount of water. If the average amount of water is 57,000,000 gallons, how much water was in the reservoir after the drought?

23

Choose a method: Set up an equation.

Think: What number is 66 % of 57,000,000?23

w = 66 % 57,000,000 Set up an equation.23

w = 57,000,000 66 % is equivalent to . 23

23

23

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The reservoir contained 38,000,000 gallons of water after the drought.

w = = 38,000,000 114,000,000

3 Simplify.

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After a drought, a river had only 50 % of the average amount of water flow. If the average amount of water flow is 60,000,000 gallons per day, how much water was flowing in the river after the drought?

23

Choose a method: Set up an equation.

Think: What number is 50 % of 60,000,000?23

w = 50 % 60,000,000 Set up an equation.23

w = 0.506 60,000,000 50 % is equivalent to 0.506. 23

w = 30,400,000 Simplify.

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Check It Out: Example 3A Continued

The water flow in the river was 30,400,000 gallons per day after the drought.

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Ms. Marvin has a savings account with approximately $214,000 in it. Mr. Parson has 35% of the amount of Ms. Marvin’s savings account. To the nearest thousand, what is the amount of Mr. Parson’s savings account?

Choose a method: Set up a proportion.

= 35

100 s

214,000 Set up a proportion.

35 214,000 = 100 s Find the cross products.

Think: 35 is to 100 as what amount is to $214,000.

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Check It Out: Example 3B Continued

Mr. Parson has approximately $75,000 in his savings account.

7,490,000 = 100s Simplify.

= 7,490,000 100

100 100


74,900 = s Simplify.

75,000 ≈ s Round to the nearest whole number.

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Lesson Quiz: Part I

Find each percent.

1. What percent of 33 is 22?

2. Of Earth’s 197 million mi2 of surface area, about

139 million mi2 is water. Find the percent of Earth’s

surface that is covered by water.

3. The Ramirez family bought a large bag of oranges

during their trip to Florida. Jorge ate of the oranges,

Ann ate 0.18 of the oranges, Mrs. Ramirez ate 22% of

the oranges, and Mr. Ramirez ate the rest. What

percent of the oranges did Mr. Ramirez eat?

70.6%

20%

66 %2 3

25

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Lesson Quiz: Part II

4. Rada is 170% as tall as her brother Raj. Raj is 0.82 m tall. To the nearest tenth of a meter, how tall is Rada?

5. The volume of Lake Superior is 2900 mi3 and

the volume of Lake Erie is 116 mi3. What

percent of the volume of Lake Superior is the

volume of Lake Erie?

1.4 m

4%

Documents

Course 3 6-3 Finding Percents 6-3 Finding Percents Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation