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Solving Percents Problems

Solving Percents Problems. Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up Solve. 1. 4 x = 90 2. 8 x = 96 3. 12 x = 180 4. 26 x = 182. 22.5. 12. 15. 7. 1. 3. Problem of the Day Rearrange the digits in . What

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Solving Percents Problems

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  1. Solving Percents Problems Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

  4. Learn to solve problems involving percents.

  5. 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.

  6. 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!

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

  8. Additional Example 1B: Using Proportions to Solve Problems with Percents Solve. 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 to isolate the variable. 25n 25 = 1,500 25 n= 60 15 is 25% of 60.

  9. 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.

  10. 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. Divide each side by 40 to isolate the variable. 40n 40 = 800 40 n= 20 8 is 40% of 20.

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

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

  13. 36 0.24 0.24 · n 0.24 = 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. Divide each side by 0.24 to isolate the variable. 150 = n 36 is 24% of 150.

  14. 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.

  15. 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. 225n 225 1800 225 = Divide each side by 225. n = 8 8% of $225 is $18. The sales tax is 8%.

  16. 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? 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%.

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. 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%

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

  20. Lesson Quiz for Student Response Systems 2. What percent of 170 is 51? A. 25% B. 30% C. 40% D. 50%

  21. Lesson Quiz for Student Response Systems 3. 128% of what number is 96? A. 25 B. 50 C. 75 D. 96

  22. Lesson Quiz for Student Response Systems 4. What percent of 1,520 is 15.2? A. 25% B. 15% C. 10% D. 1%

  23. 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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