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7-8 Solving Percents Problems Learn to solve problems involving percents.

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7-8 Solving Percents 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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7-8 Solving Percents Problems Proportion Method Equation Method n 100 = 16.5 24 Part Whole Part Whole What percent of 24 is 16.5? n · 24 = 100 · 16.5 24n = 1,650 n = 68.75 n · 24 = 16.5 n = 0.6875 n = 68.75% Sloths spend about 69% of the day sleeping!

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7-8 Solving Percents Problems Solve. Additional Example 1A: Using Proportions to Solve Problems with Percents What percent of 40 is 25? n 100 = 25 40 n · 40 = 100 · 25 40n = 2,500 40n 40 = 2,500 40 n = 62.5 25 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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7-8 Solving Percents Problems Solve. Additional Example 1B: Using Proportions to Solve Problems with Percents 15 is 25% of what number? 25 100 = 15 n n · 25 = 100 · 15 25n = 1,500 25n 25 = 1,500 25 n = 60 15 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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7-8 Solving Percents Problems Solve. Check It Out: Example 1A What percent of 50 is 10? n 100 = 10 50 n · 50 = 100 · 10 50n = 1,000 50n 50 = 1,000 50 n = 20 10 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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7-8 Solving Percents Problems Solve. Check It Out: Example 1B 8 is 40% of what number? 40 100 = 8n8n n · 40 = 100 · 8 40n = 800 40n 40 = 800 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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7-8 Solving Percents 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 35 0.28 = 0.28 · n 0.28 125 = 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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7-8 Solving Percents Problems Solve. Additional Example 2B: Using Equations to Solve Problems with Percents What percent of 9 is 18? 18 = n · 9 18 9 = n · 9 9 2 = 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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7-8 Solving Percents 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. 36 0.24 = 0.24 · n 0.24

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7-8 Solving Percents Problems Solve. Check It Out: Example 2B What percent of 6 is 36? 36 = n · 6 36 6 = n · 6 6 6 = 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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7-8 Solving Percents 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 3: Finding Sales Tax n 100 = 18 225 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 = 1800 225n 225 = 1800 225 Divide each side by 225. n = 8

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7-8 Solving Percents 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 3 n 100 = 56 800 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 = 5600 800n 800 = 5600 800 Divide each side by 800. n = 7

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