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.

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

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.

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

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.

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

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.

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.

Find a percent using the percent equation EXAMPLE 2 Find a percent using the percent equation CHECK Substitute 0.375 for p% in the original equation. 51 = p% 136 Write original equation. 51 = 0.375 136 Substitute 0.375 for p%. 51 = 51  Multiply. Solution checks.

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. = 15 88 Write percent as decimal. = 13.2 Multiply. ANSWER 13. 2 is 15% of 88.

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.

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 0.875 for p% in the original equation. 49 = p% 56 Write original equation. 49 = 0.875 56 Substitute 0.875 for p%. 49 = 49  Multiply. Solution checks.

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.

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 = 0.2 55 Substitute 0.2 for p%. 11 = 11  Multiply. Solution checks.

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. = 0.45 92 Write percent as decimal. = 41.4 Multiply. ANSWER 41.4 is 45% of 92.

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. = 1.4 50 Write percent as decimal. = 70 Multiply. ANSWER 70 is 140% of 50.

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 0.125. ANSWER 20 is 12.5% of 160.

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

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.

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

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.

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

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. 7. 65 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 0.625. ANSWER 65 is 62.5% of 104.

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. 8. 50 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.

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

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.

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.