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Finding a Number When the Percent is Known

Learn how to find a number when the percent is known. Solve various problems involving percentages and numbers.

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Finding a Number When the Percent is Known

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  1. Finding a Number When the Percent Is Known 6-4 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. 1 3 33 % Warm Up 1.What percent of 20 is 18? 2. What percent of 400 is 50? 3. 9 is what percent of 27? 4. 25 is what percent of 4? 90% 12.5% 625%

  3. Problem of the Day The original price of a sweater is $40. The sweater goes on sale for 75% of its original price. Later, the sweater goes on clearance for 50% of its sale price. What is the clearance price of the sweater? $15

  4. Learn to find a number when the percent is known.

  5. Carcharocles megalodon, a giant shark that became extinct almost 3 million years ago, had teeth as large as 7.25 inches along an edge. This is 240% bigger than the largest teeth of a modern great white shark. When one number is known, and its relationship to another number is given by a percent, the other number can be found.

  6. 12 60 12% = 100 0.12 0.12 = n 0.12 Additional Example 1: Finding a Number When the Percent Is Known 60 is 12% of what number? Choose a method: Set up an equation to find the number. 60 = 12%  n Set up an equation. 60 = 0.12n Divide both sides by 0.12. 500 = n Simplify. 60 is 12% of 500.

  7. 25 75 25% = 100 0.25 0.25 = n 0.25 Check It Out: Example 1 75 is 25% of what number? Choose an equation: Set up an equation to find the number. 75 = 25%  n Set up an equation. 75 = 0.25n Divide both sides by 0.25. 300 = n Simplify. 75 is 25% of 300.

  8. Set up a proportion. = 85 17 100 n Additional Example 2: Application Anna earned 85% on a test by answering 17 questions correctly. If each question was worth the same amount, how many questions were on the test? Choose a method: Set up a proportion to find the number. Think: 85 is to 100 as 17 is to what number?

  9. 1700 85 n = Divide both sides by 85. Additional Example 2 Continued 85  n = 100 17Find the cross products. 85n = 1700 Simplify. n = 20 Simplify. There were 20 questions on the test.

  10. Set up a proportion. = 80 20 100 n Check It Out: Example 2 Tom earned 80% on a test by answering 20 questions correctly. If each question was worth the same amount, how many questions were on the test? Choose a method: Set up a proportion to find the number. Think: 80 is to 100 as 20 is to what number?

  11. 2000 80 n = Divide both sides by 80. Check It Out: Example 2 Continued 80  n = 100 20Find the cross products. 80n = 2000 Simplify. n = 25 Simplify. There were 25 questions on the test.

  12. 55 5.2 Set up a proportion. = 100 h Additional Example 3A: Life Science Application When a giraffe is born, it is approximately 55% as tall as it will be as an adult. If a baby giraffe is 5.2 feet tall when it is born, how tall will it be when it is full grown, to the nearest tenth of a foot? Choose a method: Set up a proportion. Think: 55 is to 100 and 5.2 is to what number?

  13. 520 h Divide both sides by 55. = 55 Additional Example 3A Continued 55 h = 100 5.2Find the cross products. 55h = 520 h 9.5 Simplify. This giraffe will be approximately 9.5 feet tall when full grown.

  14. Additional Example 3B: Life Science Application A fisherman caught a lobster that weighed 11.5 lb. This was 70% of the weight of the largest lobster that fisherman had ever caught. What was the weight, to the nearest tenth of a pound, of the largest lobster the fisherman had ever caught? Choose a method: Set up an equation. Think: 11.5 is 70% of what number? 11.5 = 70% n Set up an equation.

  15. 11.5 n = Divide both sides by .70. 0.70 Additional Example 3B Continued 11.5 = 0.70 n 70% = 0.70 16.4 n Simplify. The largest lobster the fisherman had ever caught was about 16.4 lb.

  16. Check It Out: Example 3 Amy caught a fish that weighed 15.5 lb. This was 85% of the weight of the largest fish that Amy had ever caught. What was the weight, to the nearest tenth of a pound, of the largest fish that Amy had ever caught? Choose a method: Set up an equation. Think: 15.5 is 85% of what number? 15.5 = 85% n Set up an equation.

  17. 15.5 n = Divide both sides by 0.85. 0.85 Check It Out: Example 3 Continued 15.5 = 0.85 n 85% = 0.85 18.2 n Simplify. The largest fish that Amy had ever caught was about 18.2 lb.

  18. 85 120 Set up a proportion. = 100 w Check It Out: Example 3 When Bart was 12, he was approximately 85% of the weight he is now. If Bart was 120 lb, how heavy is he now, to the nearest tenth of a pound? Choose a method: Set up a proportion. Think: 85 is to 100 as 120 is to what number?

  19. 12000 w Divide both sides by 85. = 85 Check It Out: Example 3 Continued 85 w = 100 120 Find the cross products. 85w = 12000 Simplify. w 141.2 Bart weighs approximately 141.2 lbs.

  20. You have now seen all three types of percent problems. n 120 15 100 p 100 18 120 15 100 18n

  21. 1 2 Lesson Quiz 1. 10 is 12 % of what number? 2. 326 is 25% of what number? 3. 44% of what number is 11? 4. 290% of what number is 145? 5. Larry has 9 novels about the American Revolutionary War. This represents 15% of his total book collection. How many books does Larry have in all? 80 1304 25 50 60

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