2. Find a percent using a proportion
EXAMPLE 1
Find a percent using a proportion
What percent of 25 is 17?
SOLUTION
Write a proportion where 25 is the base and 17 is a part
of the base. = a b p
100
Write proportion. 17 25 = p
100
Substitute 17 for a and 25 for b.

3. Find a percent using a proportion
EXAMPLE 1
Find a percent using a proportion
1700 = 25p
Cross products property.
68 = p
Divide each side by 25.
17 is 68% of 25.
ANSWER

4. Use a proportion to answer the question.
GUIDED PRACTICE
for Example 1
Use a proportion to answer the question.
1. What percent of 20 is 15?
SOLUTION
Write a proportion where 20 is the base and 15 is a part
of the base. = a b p
100
Write proportion. 15 20 = p
100
Substitute 15 for a and 20 for b.

5. GUIDED PRACTICE for Example 1 1500 = 20p 75 = p ANSWER
Cross products property.
75 = p
Divide each side by p.
15 is 75% of 20.
ANSWER

6. Use a proportion to answer the question.
GUIDED PRACTICE
for Example 1
Use a proportion to answer the question.
2. What number is 30% percent of 90?
SOLUTION = a b p
100
Write proportion. a 90 = 30
100
Substitute 90 for b and 30 for p.

7. GUIDED PRACTICE for Example 1 100a = 2700 a = 27 ANSWER
Cross products property.
a = 27
Divide each side by 100.
27 is 30% of 90.
ANSWER

8. Find a percent using the percent equation
EXAMPLE 2
Find a percent using the percent equation
What percent of 136 is 51? a
= p% b
Write percent equation. 51
= p% 136
Substitute 51 for a and 136 for b.
0.375
= p%
Divide each side by 136.
37. 5
= p%.
Write decimal as percent.
ANSWER
51 is 37.5% of 136.

9. Find a percent using the percent equation
EXAMPLE 2
Find a percent using the percent equation
What percent of 136 is 51? a
= p% b
Write percent equation. 51
= p% 136
Substitute 51 for a and 136 for b.
0.375
= p%
Divide each side by 136.
37. 5
= p%.
Write decimal as percent.
ANSWER
51 is 37.5% of 136.

10. Find a percent using the percent equation
EXAMPLE 2
Find a percent using the percent equation
CHECK
Substitute for p% in the original
equation. 51
= p% 136
Write original equation. 51 =
Substitute for p%. 51
= 51 
Multiply. Solution checks.

11. Find a part of a base using the percent equation
EXAMPLE 3
Find a part of a base using the percent equation
What number is 15% of 88?
a = p% b
Write percent equation.
= 15% 88
Substitute 15 for p and 88 for b. =
Write percent as decimal.
= 13.2
Multiply.
ANSWER
13. 2 is 15% of 88.

12. GUIDED PRACTICE for Examples 2 and 3 3. What percent of 56 is 49? a
= p% b
Write percent equation. 49
= p% 56
Substitute 49 for a and 56 for b.
0.875
= p%
Divide each side by 56.
87. 5
= p%.
Write decimal as percent.
ANSWER
49 is 87.5% of 56.

13. Find a percent using the percent equation for Examples 2 and 3
GUIDED PRACTICE
Find a percent using the percent equation
for Examples 2 and 3
CHECK
Substitute for p% in the original
equation. 49
= p% 56
Write original equation. 49 =
Substitute for p%. 49
= 49 
Multiply. Solution checks.

14. GUIDED PRACTICE for Examples 2 and 3 4. What percent of 55 is 11? a
= p% b
Write percent equation. 11
= p% 55
Substitute 11 for a and 55 for b.
0.2
= p%
Divide each side by 55. 20
= p%.
Write decimal as percent.
ANSWER
11 is 20% of 55.

15. Find a percent using the percent equation for Examples 2 and 3
GUIDED PRACTICE
Find a percent using the percent equation
for Examples 2 and 3
CHECK
Substitute 0.2 for p% in the original
equation. 11
= p% 55
Write original equation. 11 =
Substitute 0.2 for p%. 11
= 11 
Multiply. Solution checks.

16. Find a part of a base using the percent equation for Examples 2 and 3
GUIDED PRACTICE
Find a part of a base using the percent equation
for Examples 2 and 3
5. What number is 45% of 92?
a = p% b
Write percent equation.
= 45% 92
Substitute 45 for p and 92 for b. =
Write percent as decimal.
= 41.4
Multiply.
ANSWER
41.4 is 45% of 92.

17. Find a part of a base using the percent equation for Examples 2 and 3
GUIDED PRACTICE
Find a part of a base using the percent equation
for Examples 2 and 3
6. What number is 140% of 50?
a = p% b
Write percent equation.
= 140% 50
Substitute 140 for p and 50 for b. =
Write percent as decimal.
= 70
Multiply.
ANSWER
70 is 140% of 50.

18. Find a base using the percent equation
EXAMPLE 4
Find a base using the percent equation
20 is 12.5% of what number?
a =
p% b
Write percent equation.
20 =
12.5% b
Substitute 20 for a and 12.5 for p.
20 =
0.125% b
Write percent as decimal.
160 = b
Divide each side by
ANSWER
20 is 12.5% of 160.

19. 83 EXAMPLE 5 Solve a real-world percent problem Type of Pasta Students
Survey
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.
a. macaroni and cheese
b. lasagna

20. Solve a real-world percent problem
EXAMPLE 5
Solve a real-world percent problem
SOLUTION
The survey results show that 33 of the 220 students chose macaroni and cheese. a. a
= p% b
Write percent equation.
33 =
p% 220
Substitute 33 for a and 220 for b.
0.15 = p%
Divide each side by 220.
15% = p%
Write decimal as percent.

21. EXAMPLE 5
Solve a real-world percent problem
ANSWER
15% of the students chose macaroni and cheese as their favorite dish.

22. Solve a real-world percent problem
EXAMPLE 5
Solve a real-world percent problem
b. The survey results show that 40 of the 220 students
chose lasagna.
a =
p% b
Write percent equation.
40 =
p% 220
Substitute 40 for a and 220 for b.
0 18 p%
Divide each side by 220. 18 p%
Write decimal as percent.

23. EXAMPLE 5
Solve a real-world percent problem
About 18% of the students chose lasagna
as their favorite dish.
ANSWER

24. Find a base using the percent equation for Examples 4 and 5
GUIDED PRACTICE
Find a base using the percent equation
for Examples 4 and 5
In exercises 7 and 8, use the percent equation to answer the question.
is 62.5% of what number ?
a =
p% b
Write percent equation.
65 =
62.5% b
Substitute 65 for a and 62.5 for p.
65 =
0.625% b
Write percent as decimal.
104 = b
Divide each side by
ANSWER
65 is 62.5% of 104.

25. Find a base using the percent equation for Examples 4 and 5
GUIDED PRACTICE
Find a base using the percent equation
for Examples 4 and 5
In exercises 7 and 8, use the percent equation to answer the question.
is 125% of what number ?
a =
p% b
Write percent equation.
50 =
125% b
Substitute 50 for a and 125 for p.
50 =
1.25 b
Write percent as decimal.
40 = b
Divide each side by 1.25.
ANSWER
50 is 125% of 40.

26. 83 EXAMPLE 5 GUIDED PRACTICE Solve a real-world percent problem
for Examples 4 and 5
SURVEY
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.
a. macaroni and cheese
b. lasagna

27. Solve a real-world percent problem for Examples 4 and 5
GUIDED PRACTICE
Solve a real-world percent problem
for Examples 4 and 5
SOLUTION
In example 5, what percent of students chose fettucine alfredo? 9. a
= p% b
Write percent equation.
22 =
p% 220
Substitute 22 for a and 220 for b.
0.1= p%
Divide each side by 220.
10% = p%
Write decimal as percent.

28. EXAMPLE 5
GUIDED PRACTICE
Solve a real-world percent problem
for Examples 4 and 5
ANSWER
10% of the students chose fettucine alfredo as their favorite dish.