This document provides examples for solving different types of percent problems: 1) Finding a number when the percent is known by setting up equations. 2) Applications involving finding a whole number when a percentage and part are given using proportions. 3) Life science applications involving finding a whole based on a given percentage and part using proportions. The document includes examples step-by-step solutions and check problems for students to practice the different percent problem types.

1. Warm Up California Standards Lesson Presentation Preview

2. 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. NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications . California Standards

4. When one number is known, and its relationship to another number is given by a percent, the other number can be found.

5. 60 = 0.12 n 60 is 12% of what number? Additional Example 1: Finding a Number When the Percent Is Known Choose a method: Set up an equation. 60 = 12%  n Divide both sides by 0.12. 500 = n 60 is 12% of 500. Let n represent the whole. 12% = 0.12 Simplify. part = percent  whole Set up an equation. = n 60 0.12 0.12 0.12

6. 75 = 0.25 n 75 is 25% of what number? Check It Out! Example 1 Choose a method: Set up an equation. 75 = 25%  n Divide both sides by 0.25. 300 = n 75 is 25% of 300. Let n represent the whole. 25% = 0.25 Simplify. part = percent  whole Set up an equation. = n 75 0.25 0.25 0.25

7. 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. Think: 85 is to 100 as 17 is to what number ? 85  n = 100  17 Find the cross products. 85 n = 1700 Simplify. = 85 100 17 n Set up a proportion.

8. Additional Example 2 Continued There were 20 questions on the test. Divide both sides by 85. n = 20 Simplify. 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? 85 n = 1700 85 85

9. Check It Out! Example 2 Choose a method : Set up a proportion. Think: 80 is to 100 as 20 is to what number ? 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? 80  n = 100  20 Find the cross products. 80 n = 2000 Simplify. = 80 100 20 n Set up a proportion.

10. Check It Out! Example 2 Continued There were 25 questions on the test. Divide both sides by 80. n = 25 Simplify. 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? 80 n = 2000 80 80

11. 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? 55  h = 100  5.2 Find the cross products. = h 5.2 55 100 Set up a proportion.

12. Additional Example 3A Continued This giraffe will be approximately 9.5 feet tall when full grown. h  9.5 Simplify. 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? 520 55 h = Divide both sides by 55.

13. 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. 11.5 = 0.70  n 70% = 0.70

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

15. 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 3A 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 = 0.85  n 85% = 0.85

16. Check It Out! Example 3A Continued 18.2  n The largest fish that Amy had ever caught was about 18.2 lb. Simplify. 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? Divide both sides by 0.85. 15.5 0.85 n =

17. 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 3B Choose a method : Set up a proportion. Think: 85 is to 100 as 120 is to what number? 85 w = 12,000 Simplify. 85  w = 100  120 Find the cross products. = w 120 85 100 Set up a proportion.

18. Bart weighs approximately 141.2 lbs. w  141.2 Check It Out! Example 3B Continued Simplify. 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? 12000 85 w = Divide both sides by 85.

19. You have now seen all three types of percent problems.

20. 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 60 1 2