Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to find 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.

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. 12 100 12% = 60 = 0.12n = n 60 0.12 Divide both sides by 0.12. 500 = n Simplify. 60 is 12% of 500.

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. 25 100 25% = 75 = 0.25n = n 75 0.25 Divide both sides by 0.25. 300 = n Simplify. 75 is 25% of 300.

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? = 85 100 17 n Set up a proportion.

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

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? = 80 100 20 n Set up a proportion.

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

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? = h 5.2 55 100 Set up a proportion.

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

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.

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

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.

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

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? = w 120 85 100 Set up a proportion.

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

You have now seen all three types of percent problems.

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 21

Lesson Quiz 1 2 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

Lesson Quiz for Student Response Systems 1. 18 is 37.5% of what number? A. 36 B. 48 C. 72 D. 75 23

Lesson Quiz for Student Response Systems 2. 435 is 30% of what number? A. 1400 B. 1415 C. 1450 D. 1480 24

Lesson Quiz for Student Response Systems 3. 175% of what number is 56? A. 25 B. 29 C. 32 D. 36 25

Lesson Quiz for Student Response Systems 4. Isaac has 15 cartoon CDs. This represents 20% of his total CD collection. How many CDs does Isaac have in all? A. 60 CDs B. 64 CDs C. 70 CDs D. 75 CDs 26