1. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. California Standards

2. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known When one number is known, and its relationship to another number is given by a percent, the other number can be found.

3. Evaluating Algebraic Expressions 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. 60 = 12%  n = n 60 0.12 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.

4. Evaluating Algebraic Expressions 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 a method: Set up an equation. 75 = 25%  n = n 75 0.25 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.

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

6. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known Additional Example 2 Continued There were 20 questions on the test. Divide both sides by 85. n = 20Simplify. 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

7. Evaluating Algebraic Expressions 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. 55  h = 100  5.2 Find the cross products.

8. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known Additional Example 3A Continued This giraffe will be approximately 9.5 feet tall when full grown. 520 55 h = Divide both sides by 55. 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?

9. Evaluating Algebraic Expressions 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. 11.5 = 0.70  n 70% = 0.70

10. Evaluating Algebraic Expressions 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. Divide both sides by 0.70. 11.5 0.70 n = 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?

11. Evaluating Algebraic Expressions 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 3B 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. 85w = 12,000 Simplify. 85  w = 100  120 Find the cross products.

12. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known Bart weighs approximately 141.2 lbs. 12000 85 w = Divide both sides by 85. 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?

13. Evaluating Algebraic Expressions 6-4 Finding a Number When the Percent Is Known You have now seen all three types of percent problems.