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

2. Course 3 6-4 Finding a Number When the Percent Is Known 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% 33 1 3 %

3. Course 3 6-4 Finding a Number When the Percent Is Known 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. Course 3 6-4 Finding a Number When the Percent Is Known Learn to find a number when the percent is known.

5. Course 3 6-4 Finding a Number When the Percent Is Known 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. Course 3 6-4 Finding a Number When the Percent Is Known 60 = 0.12n 60 is 12% of what number? Additional Example 1: Finding a Number When the Percent Is Known Choose a method: Set up an equation to find the number. 60 = 12%  n = n 60 0.12 Divide both sides by 0.12. 500 = n 60 is 12% of 500. Set up an equation. 12 100 12% = Simplify.

7. Course 3 6-4 Finding a Number When the Percent Is Known 75 = 0.25n 75 is 25% of what number? Check It Out: Example 1 Choose an equation: Set up an equation to find the number. 75 = 25%  n = n 75 0.25 Divide both sides by 0.25. 300 = n 75 is 25% of 300. Set up an equation. 25 100 25% = Simplify.

8. Course 3 6-4 Finding a Number When the Percent Is Known 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? Additional Example 2: Application Choose a method: Set up a proportion to find the number. Think: 85 is to 100 as 17 is to what number? = 85 100 17 n Set up a proportion.

9. Course 3 6-4 Finding a Number When the Percent Is Known Additional Example 2 Continued There were 20 questions on the test. 85  n = 100  17 Find the cross products. 85 n = 1700 n = Divide both sides by 85. 1700 85 n = 20 Simplify.

10. Course 3 6-4 Finding a Number When the Percent Is Known Check It Out: Example 2 Choose a method: Set up a proportion to find the number. Think: 80 is to 100 as 20 is to what number? = 80 100 20 n Set up a proportion. 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?

11. Course 3 6-4 Finding a Number When the Percent Is Known Check It Out: Example 2 Continued There were 25 questions on the test. 80  n = 100  20 Find the cross products. 80 n = 2000 n = Divide both sides by 80. 2000 80 n = 25 Simplify.

12. Course 3 6-4 Finding a Number When the Percent Is Known 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? Additional Example 3A: Life Science Application Choose a method: Set up a proportion. Think: 55 is to 100 and 5.2 is to what number? = h 5.2 55 100 Set up a proportion.

13. Course 3 6-4 Finding a Number When the Percent Is Known Additional Example 3A Continued 55h = 520 This giraffe will be approximately 9.5 feet tall when full grown. 55  h = 100  5.2 Find the cross products. 520 55 h = Divide both sides by 55. h  9.5 Simplify.

14. Course 3 6-4 Finding a Number When the Percent Is Known 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? Additional Example 3B: Life Science Application Choose a method: Set up an equation. Think: 11.5 is 70% of what number? 11.5 = 70%  n Set up an equation.

15. Course 3 6-4 Finding a Number When the Percent Is Known Additional Example 3B Continued 16.4  n The largest lobster the fisherman had ever caught was about 16.4 lb. 11.5 = 0.70  n 70% = 0.70 Divide both sides by.70. 11.5 0.70 n = Simplify.

16. Course 3 6-4 Finding a Number When the Percent Is Known 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? Check It Out: Example 3 Choose a method: Set up an equation. Think: 15.5 is 85% of what number? 15.5 = 85%  n Set up an equation.

17. Course 3 6-4 Finding a Number When the Percent Is Known Check It Out: Example 3 Continued 18.2  n The largest fish that Amy had ever caught was about 18.2 lb. 15.5 = 0.85  n 85% = 0.85 Divide both sides by 0.85. 15.5 0.85 n = Simplify.

18. Course 3 6-4 Finding a Number When the Percent Is Known 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? Check It Out: Example 3 Choose a method: Set up a proportion. Think: 85 is to 100 as 120 is to what number? = w 120 85 100 Set up a proportion.

19. Course 3 6-4 Finding a Number When the Percent Is Known 85w = 12000 Bart weighs approximately 141.2 lbs. 85  w = 100  120 Find the cross products. 12000 85 w = Divide both sides by 85. w  141.2 Check It Out: Example 3 Continued Simplify.

20. Course 3 6-4 Finding a Number When the Percent Is Known Three Types of Percent Problems 1. Finding the percent of a number. 15% of 120 = n = 2. Finding the percent one number is of another. p% of 120 = 18 = 3. Finding a number when the percent is known. 15% of n = 18 = You have now seen all three types of percent problems. 15 100 n 120 18 120 p 100 18 n 15 100

21. Course 3 6-4 Finding a Number When the Percent Is Known 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? 1304 80 25 50 1 2 60