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Pre-Algebra
8-3 Finding a Number When the Percent Is Known8-3 Finding a Number When the
Percent Is Known
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
8-3 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%
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
625%
331
3 %
Pre-Algebra
8-3 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
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Learn to find a number when the percent is known.
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
The Pacific giant squid can grow to a weight of 2000 pounds. This is 1250% of the maximum weight of the Pacific giant octopus. When one number is known, and is relationship to another number is given by a percent, the other number can be found.
Pre-Algebra
8-3 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
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% =
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
75 = 0.25n
75 is 25% of what number?
Try This: Example 1
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% =
Pre-Algebra
8-3 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.
Pre-Algebra
8-3 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 = Solve for n.1700
85
n = 20
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Try This: 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?
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Try This: Example 2 Continued
There were 25 questions on the test.
80 n = 100 20 Find the cross products.
80 n = 2000
n = Solve for n.2000
80
n = 25
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
A. 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 3A: 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.
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Additional Example 3A 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
Solve for n. 11.5 0.70
n=
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
B. When a giraffe is born, 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 3B: 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.
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Additional Example 3B 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 = Solve for h.
h 9.5
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
A. 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?
Try This: 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.
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
Try This: 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
Solve for n. 15.5 0.85
n=
Pre-Algebra
8-3 Finding a Number When the Percent Is Known
B. 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?
Try This: 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.
Pre-Algebra
8-3 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 = Solve for h.
w 141.2
Try This: Example 3 Continued
Pre-Algebra
8-3 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.
Pre-Algebra
8-3 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