3.7 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Percent Problems

3.7 Warm-Up ANSWER 0.27 Write the percentage as a decimal 1. 27% ANSWER % ANSWER ANSWER = n 4. = y Solve the proportion.

3.7 Warm-Up ANSWER 12 balls 5. A tennis ball machine throws 2 balls every 3 seconds. How many balls will the machine throw in 18 seconds?

3.7 Example 1 Substitute 17 for a and 25 for b. Write proportion. Write a proportion where 25 is the base and 17 is a part of the base. SOLUTION What percent of 25 is 17? = a b p = p is 68% of 25. ANSWER 68 = p 1700 = 25p Divide each side by 25. Cross products property.

3.7 Guided Practice 1. What percent of 20 is 15? Use a proportion to answer the question. 75% ANSWER 2. What number is 30% percent of 90? 27 ANSWER

3.7 Example 2 Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. What percent of 136 is 51? ANSWER 51 is 37.5% of = p% 37.5= p% 51 = p% 136 a = p% b

3.7 Example 2 Multiply. Solution checks. Substitute for p%. Write original equation. CHECK Substitute for p% in the original equation. 51 = p% = = 51

3.7 Example 3 Multiply. Write percent as decimal. Substitute 15 for p and 88 for b. Write percent equation. What number is 15 % of 88? = 13.2 ANSWER 13.2 is 15% of 88. a = p% b = 15% 88 = 0.15 · 88

3.7 Guided Practice 3. What percent of 56 is 49? ANSWER 87.5% Use the percent equation to answer the question. 4. What percent of 55 is 11? ANSWER 20% 5. What number is 45% of 92? ANSWER What number is 140% of 50? ANSWER 70

3.7 Example 4 Divide each side by Write percent as decimal. Substitute 20 for a and 12.5 for p. Write percent equation. 20 is 12.5% of what number? ANSWER 20 is 12.5% of = b a =a = p% bp% b 20 = 12.5% b 20 = · b

3.7 Guided Practice is 62.5% of what number ? ANSWER 104 In Exercises 7 and 8, use the percent equation to answer the question is 125% of what number ? ANSWER 40

3.7 Example 5 b. lasagna a. macaroni and cheese A survey asked 220 students to name their favorite pasta dish. Find the percent of students who chose the given pasta dish. Survey

3.7 Example 5 Write decimal as percent. 15% = p% Divide each side by 220. Substitute 33 for a and 220 for b. Write percent equation = p% SOLUTION The survey results show that 33 of the 220 students chose macaroni and cheese. a. a = p% b 33 = p% 220 ANSWER 15% of the students chose macaroni and cheese as their favorite dish.

3.7 Example 5 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. 18% p% 0.18 p% a =a = p% b 40 = p% 220 About 18% of the students chose lasagna as their favorite dish. ANSWER

3.7 Guided Practice In Example 5, what percent of students chose fettucine alfredo ? 9. ANSWER 10%

3.7 Lesson Quiz 2. What percent of 128 is 48 ? 37.5% ANSWER Solve the percent problem 1. What percent of 50 is 1 ? ANSWER 2% 3. What number is 16% of 45 ? ANSWER is 12.5% of what number? ANSWER 96

3.7 Lesson Quiz Leonard has read 1001 pages out of 1456 of Tolstoy’s War and Peace. What percent of the novel has he read? 5.5. ANSWER 68.75%