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California Standards

California Standards. NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Also covered: NS1.3, AF1.1.

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California Standards

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  1. California Standards NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Also covered:NS1.3, AF1.1

  2. 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.

  3. Proportion Method Equation Method n Part Part 16.5 = What percent of 24 is 16.5? Whole 24 Whole 100 n · 24 = 100 · 16.5 n · 24 = 16.5 24n = 1,650 n = 0.6875 n = 68.75 n = 68.75% Sloths spend about 69% of the day sleeping!

  4. Additional Example 1: Using Proportions to Solve Problems with Percents Solve. A. 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. n = 62.5 25 is 62.5% of 40.

  5. Additional Example 1: Using Proportions to Solve Problems with Percents Solve. B. 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. Divide each side by 25. 25n 25 = 1,500 25 n = 60 15 is 25% of 60.

  6. Check It Out! Example 1 Solve. A. 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. n = 20 10 is 20% of 50.

  7. Check It Out! Example 1 Solve. B. 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. Divide each side by 40. 40n 40 = 800 40 n = 20 8 is 40% of 20.

  8. Additional Example 2: Using Equations to Solve Problems with Percents Solve. A. 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. 125 = n 35 is 28% of 125.

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

  10. 36 0.24 0.24 · n 0.24 = Check It Out! Example 2 Solve. A. 36 is 24% of what number? 36 = 24% · n Write an equation. 36 = 0.24 · n Write 24% as a decimal. Divide each side by 0.24. 150 = n 36 is 24% of 150.

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

  12. Additional Example 3: 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. 1800 225 225n 225 Divide each side by 225. = n= 8 8% of $225 is $18. The sales tax is 8%.

  13. Helpful Hint The sales tax rate is the percent used to calculate sales tax.

  14. Check It Out! Example 3 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? 56 800 n 100 = Write a proportion. n·800=100·56 Set the cross products equal. 800n = 5600 Multiply. 5600 800 800n 800 Divide each side by 800. = n = 7 7% of $800 is $56. The sales tax is 7%.

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