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Substitute 17 for a and 25 for b.
Write proportion.
Write a proportion where 25 is the base and 17 is a partof the base.
SOLUTION
Find a percent using a proportion
EXAMPLE 1
What percent of 25 is 17?
=a
b p
100
17 25 =
p 100
17 is 68% of 25.ANSWER
68 = p
1700 = 25p
Divide each side by 25.
Cross products property.
Find a percent using a proportion
EXAMPLE 1
Substitute 15 for a and 20 for b.
Write proportion.
Write a proportion where 20 is the base and 15 is a partof the base.
SOLUTION
1. What percent of 20 is 15?
GUIDED PRACTICE for Example 1
15 20 =
p 100
=a
b
p 100
Use a proportion to answer the question.
15 is 75% of 20.ANSWER
75 = p
1500 = 20p
Divide each side by p.
Cross products property.
GUIDED PRACTICE for Example 1
Substitute 90 for b and 30 for p.
Write proportion.
SOLUTION
2. What number is 30% percent of 90?
=a
b p
100
GUIDED PRACTICE for Example 1
a 90 =
30 100
Use a proportion to answer the question.
27 is 30% of 90.ANSWER
a = 27
100a = 2700
Divide each side by 100.
Cross products property.
GUIDED PRACTICE for Example 1
Write decimal as percent.
Divide each side by 136.
Substitute 51 for a and 136 for b.
Write percent equation.
Find a percent using the percent equation
EXAMPLE 2
What percent of 136 is 51?
ANSWER 51 is 37.5% of 136.
0.375 = p%
37. 5= p%.
51 = p% 136
a = p% b
Write decimal as percent.
Divide each side by 136.
Substitute 51 for a and 136 for b.
Write percent equation.
Find a percent using the percent equation
EXAMPLE 2
What percent of 136 is 51?
ANSWER 51 is 37.5% of 136.
0.375 = p%
37. 5= p%.
51 = p% 136
a = p% b
Multiply. Solution checks.
Substitute 0.375 for p%.
Write original equation.
Find a percent using the percent equation
EXAMPLE 2
CHECK Substitute 0.375 for p% in the original equation.
51 = 51
51 = p% 136
51 = 0.375 136
Multiply.
Write percent as decimal.
Substitute 15 for p and 88 for b.
Write percent equation.
Find a part of a base using the percent equation
EXAMPLE 3
What number is 15% of 88?
= 13.2
ANSWER 13. 2 is 15% of 88.
a = p% b
= 15% 88
= 15 88
Write decimal as percent.
Divide each side by 56.
Substitute 49 for a and 56 for b.
Write percent equation.
3. What percent of 56 is 49?
ANSWER 49 is 87.5% of 56.
0.875 = p%
87. 5= p%.
GUIDED PRACTICE for Examples 2 and 3
a = p% b
49 = p% 56
Multiply. Solution checks.
Substitute 0.875 for p%.
Write original equation.
Find a percent using the percent equation
EXAMPLE 2
CHECK Substitute 0.875 for p% in the original equation.
49 = 49
GUIDED PRACTICE for Examples 2 and 3
49 = p% 56
49 = 0.875 56
Write decimal as percent.
Divide each side by 55.
Substitute 11 for a and 55 for b.
Write percent equation.
4. What percent of 55 is 11?
ANSWER 11 is 20% of 55.
0.2 = p%
20 = p%.
GUIDED PRACTICE for Examples 2 and 3
11 = p% 55
a = p% b
Multiply. Solution checks.
Substitute 0.2 for p%.
Write original equation.
Find a percent using the percent equation
EXAMPLE 2
CHECK Substitute 0.2 for p% in the original equation.
11 = 11
GUIDED PRACTICE for Examples 2 and 3
11 = p% 55
11 = 0.2 55
Multiply.
Write percent as decimal.
Substitute 45 for p and 92 for b.
Write percent equation.
Find a part of a base using the percent equation
EXAMPLE 3
5. What number is 45% of 92?
= 41.4
ANSWER 41.4 is 45% of 92.
GUIDED PRACTICE for Examples 2 and 3
a = p% b
= 45% 92
= 0.45 92
Multiply.
Write percent as decimal.
Substitute 140 for p and 50 for b.
Write percent equation.
Find a part of a base using the percent equation
EXAMPLE 3
6. What number is 140% of 50?
= 70
ANSWER 70 is 140% of 50.
GUIDED PRACTICE for Examples 2 and 3
a = p% b
= 140% 50
= 1.4 50
Divide each side by 0.125.
Write percent as decimal.
Substitute 20 for a and 12.5 for p.
Write percent equation.
20 is 12.5% of what number?
Find a base using the percent equation
EXAMPLE 4
ANSWER 20 is 12.5% of 160.
160 = b
a = p% b
20 = 12.5% b
20 = 0.125% b
b. lasagna
a. macaroni and cheese
Solve a real-world percent problem
EXAMPLE 5
Type of Pasta Students
Spaghetti 83
Lasagna 40
Macaroni and cheese
33
Fettucine alfredo
22
Baked ziti 16
Pasta primavera
15
Other 11
A survey asked 220 students to name their favorite pasta dish. Find the percent of students who chose the given pasta dish.
Survey
Write decimal as percent. 15% = p%
Divide each side by 220.
Substitute 33 for a and 220 for b.
Write percent equation.
SOLUTION
Solve a real-world percent problem
EXAMPLE 5
0.15 = p%
The survey results show that 33 of the 220 students chose macaroni and cheese.
a.
a = p% b
33 = p% 220
Solve a real-world percent problemEXAMPLE 5
ANSWER
15% of the students chose macaroni and cheese as their favorite dish.
Write decimal as percent.
Divide each side by 220.
Substitute 40 for a and 220 for b.
Write percent equation.
b. The survey results show that 40 of the 220 students chose lasagna.
Solve a real-world percent problemEXAMPLE 5
18 p%
0 18 p%
a = p% b
40 = p% 220
About 18% of the students chose lasagna as their favorite dish.
ANSWER
Solve a real-world percent problemEXAMPLE 5
Divide each side by 0.625.
Write percent as decimal.
Substitute 65 for a and 62.5 for p.
Write percent equation.
7. 65 is 62.5% of what number ?
Find a base using the percent equationEXAMPLE 4
ANSWER 65 is 62.5% of 104.
104 = b
GUIDED PRACTICE for Examples 4 and 5
a = p% b
65 = 62.5% b
65 = 0.625% b
In exercises 7 and 8, use the percent equation to answer the question.
Divide each side by 1.25.
Write percent as decimal.
Substitute 50 for a and 125 for p.
Write percent equation.
8. 50 is 125% of what number ?
Find a base using the percent equationEXAMPLE 4
ANSWER 50 is 125% of 40.
40 = b
GUIDED PRACTICE for Examples 4 and 5
a = p% b
50 = 125% b
50 = 1.25 b
In exercises 7 and 8, use the percent equation to answer the question.
b. lasagna
a. macaroni and cheese
Solve a real-world percent problem
EXAMPLE 5
Type of Pasta Students
Spaghetti 83
Lasagna 40
Macaroni and cheese
33
Fettucine alfredo
22
Baked ziti 16
Pasta primavera
15
Other 11
SURVEY
A survey asked 220 students to name their favorite pasta dish. Find the percent of students who chose the given pasta dish.
GUIDED PRACTICE for Examples 4 and 5
Write decimal as percent. 10% = p%
Divide each side by 220.
Substitute 22 for a and 220 for b.
Write percent equation.
In example 5, what percent of students chose fettucine alfredo?
9.
SOLUTION
Solve a real-world percent problemEXAMPLE 5
0.1=p%
GUIDED PRACTICE for Examples 4 and 5
22 = p% 220
a = p% b
Solve a real-world percent problemEXAMPLE 5
ANSWER
10% of the students chose fettucine alfredo as their favorite dish.
GUIDED PRACTICE for Examples 4 and 5
