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6-5 Solving Percent Problems Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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6-5 Solving Percent Problems Warm Up Solve. 1. 4x = x = x = x =

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6-5 Solving Percent Problems Problem of the Day Rearrange the digits in. What fraction of the possible arrangements are true proportions? 2626 =

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6-5 Solving Percent Problems MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes… Sunshine State Standards

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6-5 Solving Percent Problems Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day 16.5 hours is, you can use a proportion or an equation.

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6-5 Solving Percent Problems Proportion Method Equation Method n 100 = Part Whole Part Whole What percent of 24 is 16.5? n · 24 = 100 · n = 1,650 n = n · 24 = 16.5 n = n = 68.75% Sloths spend about 69% of the day sleeping!

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6-5 Solving Percent Problems Solve. Additional Example 1A: Using Proportions to Solve Problems with Percents What percent of 40 is 25? n 100 = n · 40 = 100 · 25 40n = 2,500 40n 40 = 2, n = is 62.5% of 40. Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to isolate the variable.

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6-5 Solving Percent Problems Solve. Additional Example 1B: Using Proportions to Solve Problems with Percents 15 is 25% of what number? = 15 n n · 25 = 100 · 15 25n = 1,500 25n 25 = 1, n = is 25% of 60. Write a proportion. Set the cross products equal. Multiply. Divide each side by 25 to isolate the variable.

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6-5 Solving Percent Problems Solve. Check It Out: Example 1A What percent of 50 is 10? n 100 = n · 50 = 100 · 10 50n = 1,000 50n 50 = 1, n = is 20% of 50. Write a proportion. Set the cross products equal. Multiply. Divide each side by 50 to isolate the variable.

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6-5 Solving Percent Problems Solve. Check It Out: Example 1B 8 is 40% of what number? = 8n8n n · 40 = 100 · 8 40n = n 40 = n = 20 8 is 40% of 20. Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to isolate the variable.

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6-5 Solving Percent Problems Solve. Additional Example 2A: Using Equations to Solve Problems with Percents 35 is 28% of what number? 35 = 28% · n 35 = 0.28 · n = 0.28 · n = n 35 is 28% of 125. Write an equation. Write 28% as a decimal. Divide each side by 0.28 to isolate the variable.

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6-5 Solving Percent Problems Solve. Additional Example 2B: Using Equations to Solve Problems with Percents What percent of 9 is 18? 18 = n · = n · = n 200% = n 18 is 200% of 9. Write an equation. Divide each side by 9 to isolate the variable. Write the decimal as a percent.

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6-5 Solving Percent Problems Solve. Check It Out: Example 2A 36 is 24% of what number? 36 = 24% · n 36 = 0.24 · n 150 = n 36 is 24% of 150. Write an equation. Write 24% as a decimal. Divide each side by 0.24 to isolate the variable = 0.24 · n 0.24

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6-5 Solving Percent Problems Solve. Check It Out: Example 2B What percent of 6 is 36? 36 = n · = n · = n 600% = n 36 is 600% of 6. Write an equation. Divide each side by 6 to isolate the variable. Write the decimal as a percent.

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6-5 Solving Percent Problems Raoul found a pair of shoes that were marked down to 80% of the original price. He had a coupon that gave him an additional $10 off the shoes. The sales tax rate was 6.5% and Raoul paid $5.46 in sales tax. What was the original price of the pair of shoes? Additional Example 3: Consumer Application Write a word sentence. Work backward. Find the final price of the shoes. 6.5% of price is $5.46. Write an equation x = 5.46 Divide both sides by x = 84 The price of the shoes with the coupon was $84.

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6-5 Solving Percent Problems Additional Example 3 Continued Find the price of the shoes without the coupon = 94 The price of the shoes was $94 after it was marked down to 80% of the original price. Find the original price. Write a word sentence.80% of price is $94. Write an equation. 0.8 x = 94 Divide both sides by 0.8. x = The original price of the shoes was $

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6-5 Solving Percent Problems Livy found a comforter marked down to 50% of the original price. She had a coupon that gave her an additional $10 off her purchase. The sales tax rate was 8.25% and Livy paid $6.19 in sales tax. What was the original price of the comforter? Check It Out: Example 3 Write a word sentence. Work backward. Find the final price of the comforter. 8.25% of price is $6.19. Write an equation x = 6.19 Divide both sides by x = The price of the comforter with the coupon was $75.03.

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6-5 Solving Percent Problems Check It Out: Example 3 Continued Find the price of the comforter without the coupon = The price of the comforter was $85.03 after it was marked down to 50% of the original price. Find the original price. Write a word sentence.50% of price is $ Write an equation. 0.5 x = Divide both sides by 0.5. x = The original price of the comforter was $

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6-5 Solving Percent Problems A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18? Additional Example 4: Finding Sales Tax n 100 = n · 225 = 100 · 18 8% of $225 is $18. The sales tax is 8%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $225 is $18? 225n = n 225 = Divide each side by 225. n = 8

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6-5 Solving Percent Problems A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56? Check It Out: Example 4 n 100 = n · 800 = 100 · 56 7% of $800 is $56. The sales tax is 7%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $800 is $56? 800n = n 800 = Divide each side by 800. n = 7

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6-5 Solving Percent Problems Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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6-5 Solving Percent Problems Lesson Quiz Solve is 42% of what number? 2. What percent of 292 is 73? % of what number is 84? 4. What percent of 1,340 is 13.4? 5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate? 25% % 6%

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6-5 Solving Percent Problems 1. Solve. 19 is 38% of what number? A. 69 B. 50 C. 38 D. 34 Lesson Quiz for Student Response Systems

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6-5 Solving Percent Problems 2. What percent of 170 is 51? A. 25% B. 30% C. 40% D. 50% Lesson Quiz for Student Response Systems

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6-5 Solving Percent Problems % of what number is 96? A. 25 B. 50 C. 75 D. 96 Lesson Quiz for Student Response Systems

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6-5 Solving Percent Problems 4. What percent of 1,520 is 15.2? A. 25% B. 15% C. 10% D. 1% Lesson Quiz for Student Response Systems

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6-5 Solving Percent Problems 5. A jeweler has a pendant on sale for $150. If the total cost of the pendant is $160.50, what is the sales tax rate? A. 6% B. 7% C. 8% D. 9% Lesson Quiz for Student Response Systems

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