Course 3

6-4 Finding a Number When the Percent Is Known6-4 Finding a Number When the

Percent Is Known

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

6-4 Finding a Number When the Percent Is Known

Warm Up

1. What percent of 20 is 18?

2. What percent of 400 is 50?

3. 9 is what percent of 27?

4. 25 is what percent of 4?

90%

12.5%

625%

331

3 %

Course 3

6-4 Finding a Number When the Percent Is Known

Problem of the Day

The original price of a sweater is $40. The sweater goes on sale for 75% of its original price. Later, the sweater goes on clearance for 50% of its sale price. What is the clearance price of the sweater?$15

Course 3

6-4 Finding a Number When the Percent Is Known

Learn to find a number when the percent is known.

Course 3

6-4 Finding a Number When the Percent Is Known

Carcharocles megalodon, a giant shark that became extinct almost 3 million years ago, had teeth as large as 7.25 inches along an edge. This is 240% bigger than the largest teeth of a modern great white shark.

When one number is known, and its relationship to another number is given by a percent, the other number can be found.

Course 3

6-4 Finding a Number When the Percent Is Known

60 = 0.12n

60 is 12% of what number?

Additional Example 1: Finding a Number When the Percent Is Known

Choose a method: Set up an equation to find the number.

60 = 12% n

= n 60

0.12 0.12

0.12Divide both sides by 0.12.

500 = n

60 is 12% of 500.

Set up an equation.

1210012% =

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

75 = 0.25n

75 is 25% of what number?

Check It Out: Example 1

Choose an equation: Set up an equation to find the number.

75 = 25% n

= n 75

0.25 0.25

0.25 Divide both sides by 0.25.

300 = n

75 is 25% of 300.

Set up an equation.

2510025% =

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

Anna earned 85% on a test by answering 17 questions correctly. If each question was worth the same amount, how many questions were on the test?

Additional Example 2: Application

Choose a method: Set up a proportion to find the number.

Think: 85 is to 100 as 17 is to what number?

= 85

10017

nSet up a proportion.

Course 3

6-4 Finding a Number When the Percent Is Known

Additional Example 2 Continued

There were 20 questions on the test.

85 n = 100 17 Find the cross products.

85 n = 1700

n = Divide both sides by 85.1700

85

n = 20

Simplify.

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

Check It Out: Example 2

Choose a method: Set up a proportion to find the number.

Think: 80 is to 100 as 20 is to what number?

= 80

10020

nSet up a proportion.

Tom earned 80% on a test by answering 20 questions correctly. If each question was worth the same amount, how many questions were on the test?

Course 3

6-4 Finding a Number When the Percent Is Known

Check It Out: Example 2 Continued

There were 25 questions on the test.

80 n = 100 20 Find the cross products.

80 n = 2000

n = Divide both sides by 80.2000

80

n = 25

Simplify.

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

When a giraffe is born, it is approximately 55% as tall as it will be as an adult. If a baby giraffe is 5.2 feet tall when it is born, how tall will it be when it is full grown, to the nearest tenth of a foot?

Additional Example 3A: Life Science Application

Choose a method: Set up a proportion.

Think: 55 is to 100 and 5.2 is to what number?

= h

5.2 55 100

Set up a proportion.

Course 3

6-4 Finding a Number When the Percent Is Known

Additional Example 3A Continued

55h = 520

This giraffe will be approximately 9.5 feet tall when full grown.

55 h = 100 5.2 Find the cross products.

52055

h = Divide both sides by 55.

h 9.5 Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

A fisherman caught a lobster that weighed 11.5 lb. This was 70% of the weight of the largest lobster that fisherman had ever caught. What was the weight, to the nearest tenth of a pound, of the largest lobster the fisherman had ever caught?

Additional Example 3B: Life Science Application

Choose a method: Set up an equation.

Think: 11.5 is 70% of what number?

11.5 = 70% n Set up an equation.

Course 3

6-4 Finding a Number When the Percent Is Known

Additional Example 3B Continued

16.4 n

The largest lobster the fisherman had ever caught was about 16.4 lb.

11.5 = 0.70 n 70% = 0.70

Divide both sides by .70. 11.5 0.70

n =

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

Amy caught a fish that weighed 15.5 lb. This was 85% of the weight of the largest fish that Amy had ever caught. What was the weight, to the nearest tenth of a pound, of the largest fish that Amy had ever caught?

Check It Out: Example 3

Choose a method: Set up an equation.

Think: 15.5 is 85% of what number?

15.5 = 85% n Set up an equation.

Course 3

6-4 Finding a Number When the Percent Is Known

Check It Out: Example 3 Continued

18.2 n

The largest fish that Amy had ever caught was about 18.2 lb.

15.5 = 0.85 n 85% = 0.85

Divide both sides by 0.85. 15.5 0.85

n =

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

When Bart was 12, he was approximately 85% of the weight he is now. If Bart was 120 lb, how heavy is he now, to the nearest tenth of a pound?

Check It Out: Example 3

Choose a method: Set up a proportion.

Think: 85 is to 100 as 120 is to what number?

= w

120 85 100

Set up a proportion.

Course 3

6-4 Finding a Number When the Percent Is Known

85w = 12000

Bart weighs approximately 141.2 lbs.

85 w = 100 120 Find the cross products.

12000 85

w = Divide both sides by 85.

w 141.2

Check It Out: Example 3 Continued

Simplify.

Course 3

6-4 Finding a Number When the Percent Is Known

Three Types of Percent Problems

1. Finding the percent of a number.

15% of 120 = n =

2. Finding the percent one number is of another.

p% of 120 = 18 =

3. Finding a number when the percent is known.

15% of n = 18 =

You have now seen all three types of percent problems.

15 100

n 120

18 120

p 100

18 n

15 100

Course 3

6-4 Finding a Number When the Percent Is Known

Lesson Quiz

1. 10 is 12 % of what number?

2. 326 is 25% of what number?

3. 44% of what number is 11?

4. 290% of what number is 145?

5. Larry has 9 novels about the American

Revolutionary War. This represents 15% of his

total book collection. How many books does

Larry have in all?

1304

80

25

50

12

60