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Substitute 17 for a and 25 for b .

a. b. p. p. 100. 100. =. 17. =. 25. 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. Write proportion. Substitute 17 for a and 25 for b. 17 is 68% of 25. ANSWER.

christophe-alden
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Substitute 17 for a and 25 for b .

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  1. a b p p 100 100 = 17 = 25 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. Write proportion. Substitute 17 for aand 25 for b.

  2. 17is 68%of25. ANSWER EXAMPLE 1 Find a percent using a proportion 1700 = 25p Cross products property. 68 = p Divide each side by 25.

  3. a b p p 100 100 = 15 = 20 for Example 1 GUIDED PRACTICE 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. Write proportion. Substitute 15 for aand 20 for b.

  4. 15is 75%of20. ANSWER for Example 1 GUIDED PRACTICE 1500 = 20p Cross products property. 75 = p Divide each side by p.

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

  6. 27is 30%of90. ANSWER for Example 1 GUIDED PRACTICE 100a = 2700 Cross products property. a = 27 Divide each side by 100.

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

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

  9. 51 =p% 136 51 = 0.375136 51 = 51  EXAMPLE 2 Find a percent using the percent equation CHECK Substitute 0.375 for p% in the original equation. Write original equation. Substitute 0.375 for p%. Multiply. Solution checks.

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

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

  12. 49 =p% 56 49 = 0.87556 49 = 49  EXAMPLE 2 for Examples 2 and 3 Find a percent using the percent equation GUIDED PRACTICE CHECK Substitute 0.875 for p% in the original equation. Write original equation. Substitute 0.875 for p%. Multiply. Solution checks.

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

  14. 11 =p% 55 11 = 0.2 55 11 = 11  EXAMPLE 2 for Examples 2 and 3 Find a percent using the percent equation GUIDED PRACTICE CHECK Substitute 0.2 for p% in the original equation. Write original equation. Substitute 0.2 for p%. Multiply. Solution checks.

  15. a =p%b =45%92 = 0.45 92 ANSWER 41.4 is 45% of 92. EXAMPLE 3 for Examples 2 and 3 Find a part of a base using the percent equation GUIDED PRACTICE 5.What number is 45% of 92? Write percent equation. Substitute 45 for pand 92 for b. Write percent as decimal. = 41.4 Multiply.

  16. a =p%b =140%50 = 1.4 50 ANSWER 70 is 140% of 50. EXAMPLE 3 for Examples 2 and 3 Find a part of a base using the percent equation GUIDED PRACTICE 6.What number is 140% of 50? Write percent equation. Substitute 140 for pand 50 for b. Write percent as decimal. = 70 Multiply.

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

  18. Survey EXAMPLE 5 Solve a real-world percent problem 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

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

  20. 15%of the students chose macaroni and cheese as their favorite dish. ANSWER EXAMPLE 5 Solve a real-world percent problem

  21. p% b a= p%220 40= p% 0 18 p% 18 EXAMPLE 5 Solve a real-world percent problem b. The survey results show that40of the220 students chose lasagna. Write percent equation. Substitute 40 for aand 220 for b. Divide each side by 220. Write decimal as percent.

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

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

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

  25. SURVEY EXAMPLE 5 for Examples 4 and 5 Solve a real-world percent problem GUIDED PRACTICE 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

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

  27. 10% of the students chose fettucine alfredo as their favorite dish. ANSWER EXAMPLE 5 for Examples 4 and 5 Solve a real-world percent problem GUIDED PRACTICE

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