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## Finding a Number When the Percent Is Known

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**Finding a Number When the Percent Is Known**8.3 Pre-Algebra**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%**12**60 12% = 100 0.12 0.12 = n 0.12 Example: Finding a Number When the Percent Is Known 60 is 12% of what number? 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 60 is 12% of 500.**25**75 25% = 100 0.25 0.25 = n 0.25 Try This 75 is 25% of what number? 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 75 is 25% of 300.**Set up a proportion.**= 85 17 100 n Example: 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?**1700**85 n = Solve for n. Example Continued 85 n = 100 17Find the cross products. 85n = 1700 n = 20 There were 20 questions on the test.**Set up a proportion.**= 80 20 100 n Try This 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?**2000**80 n = Solve for n. Try This Continued 80 n = 100 20Find the cross products. 80n = 2000 n = 25 There were 25 questions on the test.**Example: Life Science Application**A. 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.**11.5**n = Solve for n. 0.70 Example Continued 11.5 = 0.70 n 70% = 0.70 16.4 n The largest lobster the fisherman had ever caught was about 16.4 lb.**55**5.2 Set up a proportion. = 100 h Example: Life Science Application B.When a giraffe is born, 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?**520**h Solve for h. = 55 Example Continued 55 h = 100 5.2Find the cross products. 55h = 520 h 9.5 This giraffe will be approximately 9.5 feet tall when full grown.**Try This**A. 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.**15.5**n = Solve for n. 0.85 Try This Continued 15.5 = 0.85 n 85% = 0.85 18.2 n The largest fish that Amy had ever caught was about 18.2 lb.**85**120 Set up a proportion. = 100 w Try This B. When Bart was 12, he was approximately 85% of the weight he is now. If a 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?**12000**w Solve for h. = 85 Try This Continued 85 w = 100 120 Find the cross products. 85w = 12000 w 141.2 Bart weighs approximately 141.2 lbs.**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