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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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Warm Up Solve. 1. 4x = 90 2. 8x = 96 3. 12x = 180 4. 26x = 182 22.5 12 15 7

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**Rearrange the digits in . What **

Problem of the Day Rearrange the digits in What fraction of the possible arrangements are true proportions? 2 6 1 3 = 1 3

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**Sunshine State Standards**

MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes…

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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 hours is, you can use a proportion or an equation.

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**Proportion Method Equation Method**

Part n 16.5 Part = What percent of 24 is 16.5? Whole 100 24 Whole n · 24 = 100 · 16.5 n · 24 = 16.5 24n = 1,650 n = n = 68.75 n = 68.75% Sloths spend about 69% of the day sleeping!

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**Additional Example 1A: Using Proportions to Solve Problems with Percents**

What percent of 40 is 25? n 100 = 25 40 Write a proportion. n · 40 = 100 · 25 Set the cross products equal. 40n = 2,500 Multiply. 40n 40 = 2,500 40 Divide each side by 40 to isolate the variable. n = 62.5 25 is 62.5% of 40.

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**Additional Example 1B: Using Proportions to Solve Problems with Percents**

15 is 25% of what number? 25 100 = 15 n Write a proportion. n · 25 = 100 · 15 Set the cross products equal. 25n = 1,500 Multiply. 25n 25 = 1,500 25 Divide each side by 25 to isolate the variable. n = 60 15 is 25% of 60.

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

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Check It Out: Example 1B Solve. 8 is 40% of what number? 40 100 = 8 n Write a proportion. n · 40 = 100 · 8 Set the cross products equal. 40n = 800 Multiply. 40n 40 = 800 40 Divide each side by 40 to isolate the variable. n = 20 8 is 40% of 20.

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**Additional Example 2A: Using Equations to Solve Problems with Percents**

35 is 28% of what number? 35 = 28% · n Write an equation. 35 = 0.28 · n Write 28% as a decimal. 35 0.28 0.28 · n 0.28 Divide each side by 0.28 to isolate the variable. = 125 = n 35 is 28% of 125.

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**Additional Example 2B: Using Equations to Solve Problems with Percents**

What percent of 9 is 18? 18 = n · 9 Write an equation. 18 9 n · 9 9 Divide each side by 9 to isolate the variable. = 2 = n Write the decimal as a percent. 200% = n 18 is 200% of 9.

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

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

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**Additional Example 3: Consumer Application**

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? Work backward. Find the final price of the shoes. 6.5% of price is $5.46. Write a word sentence. 0.065 x = 5.46 Write an equation. Divide both sides by x = 84 The price of the shoes with the coupon was $84.

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**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. 80% of price is $94. Write a word sentence. 0.8 x = 94 Write an equation. Divide both sides by 0.8. x = 117.5 The original price of the shoes was $

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Check It Out: Example 3 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? Work backward. Find the final price of the comforter. 8.25% of price is $6.19. Write a word sentence. x = 6.19 Write an equation. Divide both sides by x = 75.03 The price of the comforter with the coupon was $75.03.

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**Check It Out: Example 3 Continued**

Find the price of the comforter without the coupon. = 85.03 The price of the comforter was $85.03 after it was marked down to 50% of the original price. Find the original price. 50% of price is $85.03. Write a word sentence. 0.5 x = 85.03 Write an equation. Divide both sides by 0.5. x = The original price of the comforter was $

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**Additional Example 4: Finding Sales Tax**

A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18? Restate the question: What percent of $225 is $18? n 100 18 225 = Write a proportion. n · 225 = 100 · 18 Set the cross products equal. 225n = 1800 Multiply. 225n 225 1800 225 = Divide each side by 225. n = 8 8% of $225 is $18. The sales tax is 8%.

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Check It Out: Example 4 A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56? Restate the question: What percent of $800 is $56? n 100 56 800 = Write a proportion. n · 800 = 100 · 56 Set the cross products equal. 800n = 5600 Multiply. 800n 800 5600 800 = Divide each side by 800. n = 7 7% of $800 is $56. The sales tax is 7%.

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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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Lesson Quiz Solve. 1. 21 is 42% of what number? 2. What percent of 292 is 73? 3. 112% 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? 50 25% 75 1% 6%

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**Lesson Quiz for Student Response Systems**

1. Solve. 19 is 38% of what number? A. 69 B. 50 C. 38 D. 34

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**Lesson Quiz for Student Response Systems**

2. What percent of 170 is 51? A. 25% B. 30% C. 40% D. 50%

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**Lesson Quiz for Student Response Systems**

3. 128% of what number is 96? A. 25 B. 50 C. 75 D. 96

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**Lesson Quiz for Student Response Systems**

4. What percent of 1,520 is 15.2? A. 25% B. 15% C. 10% D. 1%

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**Lesson Quiz for Student Response Systems**

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%

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