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# Chapter 8

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### Chapter 8

1. 1. Warm Up Problem of the Day Lesson Presentation 8-1 Relating Decimals, Fractions, and Percents Course 3
2. 2. Warm Up Evaluate. 1. 2. 3. 4. + 14 –  1 3 1 3 2 15 3 15 7 12 3 12 4 5 7 2 1 2 3 1 4 Course 3 8-1 Relating Decimals, Fractions, and Percents 4 5 2 14 5 or
3. 3. Problem of the Day A fast-growing flower grows to a height of 12 inches in 12 weeks by doubling its height every week. If you want your flower to be only 6 inches tall, after how many weeks should you pick it? 11 weeks Course 3 8-1 Relating Decimals, Fractions, and Percents
4. 4. Learn to relate decimals, fractions, and percents . Course 3 8-1 Relating Decimals, Fractions, and Percents
5. 5. Vocabulary percent Insert Lesson Title Here Course 3 8-1 Relating Decimals, Fractions, and Percents
6. 6. Percents are ratios that compare a number to 100. 30% 50% 75%               Percent Equivalent Ratio with Denominator of 100 Ratio 3 10 1 2 3 4 30 100 50 100 75 100 Course 3 8-1 Relating Decimals, Fractions, and Percents
7. 7. Think of the % symbol as meaning /100 . 0.75 = 75 % = 75 /100 Reading Math Course 3 8-1 Relating Decimals, Fractions, and Percents
8. 8. To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percent, multiply by 100 and insert the percent symbol. 0.125  100  12.5 % 1 8 = 1 ÷ 8 = 0.125 Course 3 8-1 Relating Decimals, Fractions, and Percents
9. 9. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents a : 10% = 1 10 10 100 = Course 3 8-1 Relating Decimals, Fractions, and Percents
10. 10. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents b : 0.25 = 25% 1 4 = Course 3 8-1 Relating Decimals, Fractions, and Percents
11. 11. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents c : 40% = 40 100 = 2 5 4 10 = Course 3 8-1 Relating Decimals, Fractions, and Percents
12. 12. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents d : 0.60 = 60% 3 5 = Course 3 8-1 Relating Decimals, Fractions, and Percents
13. 13. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents e : 2 3 % = 66 0.666 = 2 3 Course 3 8-1 Relating Decimals, Fractions, and Percents
14. 14. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents f : 0.875 = 1 2 % = 87 7 8 875 1000 = Course 3 8-1 Relating Decimals, Fractions, and Percents
15. 15. Find the missing ratio or percent equivalent for each letter a – g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents g : 125% = 125 100 = 5 4 = 1 4 1 Course 3 8-1 Relating Decimals, Fractions, and Percents
16. 16. Try This : Example 1 Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 a : 0.125 = Course 3 8-1 Relating Decimals, Fractions, and Percents 3 8 1 2 5 8 1 2 % = 12 1 8 125 1000 =
17. 17. Try This : Example 1 Continued b : 25% = Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 25 100 = 1 4 3 8 1 2 5 8
18. 18. Try This : Example 1 Continued c: 0.375 = 37 % Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 3 8 = 1 2 3 8 1 2 5 8
19. 19. Try This : Example 1 Continued d : 50% = Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 50 100 = 1 2 3 8 1 2 5 8
20. 20. Try This : Example 1 Continued e : 0.625 = 62 % Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 5 8 = 1 2 3 8 1 2 5 8
21. 21. Try This : Example 1 Continued f : 75% = Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 75 100 = 3 4 3 8 1 2 5 8
22. 22. Try This : Example 1 Continued g : 1 = = 100% Find the missing ratio or percent equivalent for each letter a – g on the number line. c a b e d 50% 12 % f g 25% 75% 1 Course 3 8-1 Relating Decimals, Fractions, and Percents 100 100 3 8 1 2 5 8
23. 23. Find the equivalent fraction, decimal, or percent for each value given on the circle graph. Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents 0.15(100) = 15% 0.12(100) = 12% 7 20 = 0.35 38%      35%         0.15   Percent Decimal Fraction 3 20 15 100 = 7 20 35 100 = 19 50 38 100 = 19 50 = 0.38 3 25 = 0.12 3 25 Course 3 8-1 Relating Decimals, Fractions, and Percents
24. 24. You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents. Additional Example 2 Continued The sum of the fractions should be 1 . The sum of the decimals should be 1 . The sum of the percents should be 100% . Course 3 8-1 Relating Decimals, Fractions, and Percents
25. 25. Try This: Example 2 Fill in the missing pieces on the chart below . 0.1(100) = 10% 0.2(100) = 20% = 0.45 = 0.25 0.25(100) = 25% = 0.2       45%       0.1   Percent Decimal Fraction 1 10 45 100 1 5 1 5 25 100 Course 3 8-1 Relating Decimals, Fractions, and Percents 1 4 45 100 9 20 =
26. 26. Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper, zinc, silver, or nickel. What percent of 14 karat gold is pure gold? Additional Example 3: Physical Science Application Set up a ratio and reduce. 7  12 = Find the percent. parts pure gold total parts 14 24 7 12 = 7 12 = 0.583 = 58.3% 1 3 So 14-karat gold is 58.3%, or 58 % pure gold. Course 3 8-1 Relating Decimals, Fractions, and Percents
27. 27. A baker’s dozen is 13. When a shopper purchases a dozen items at the bakery they get 12. It is said that the baker eats 1 item from every batch. So, what percentage of the food the baker cooks is eaten without being sold? Try This : Example 3 Set up a ratio and reduce. 1  13 = Find the percent. 0.077 = 7.7% So the baker, eats 7.7% of the items they bake. items eaten total items 1 13 1 13 = Course 3 8-1 Relating Decimals, Fractions, and Percents
28. 28. Lesson Quiz Find each equivalent value. 1. as a percent 2. 20% as a fraction 3. as a decimal 4. as a percent 5. About 342,000 km 2 of Greenland’s total area (2,175,000 km 2 ) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice? 16% 37.5% Insert Lesson Title Here 0.625 56% 3 8 14 25 1 5 5 8 Course 3 8-1 Relating Decimals, Fractions, and Percents
29. 29. Warm Up Problem of the Day Lesson Presentation 8-2 Finding Percents Course 3
30. 30. Warm Up Rewrite each value as indicated. 1. as a percent 2. 25% as a fraction 3. as a decimal 4. 0.16 as a fraction 48% 0.375 Course 3 8-2 Finding Percents 4 25 24 50 3 8 1 4
31. 31. Problem of the Day A number between 1 and 10 is halved, and the result is squared. This gives an answer that is double the original number. What is the starting number? 8 Course 3 8-2 Finding Percents
32. 32. Learn to find percents . Course 3 8-2 Finding Percents
33. 33. Relative humidity is a measure of the amount of water vapor in the air. When the relative humidity is 100%, the air has the maximum amount of water vapor. At this point, any additional water vapor would cause precipitation. To find the relative humidity on a given day, you would need to find a percent. Course 3 8-2 Finding Percents
34. 34. Additional Example 1A: Finding the Percent One Number Is of Another A. What percent of 220 is 88? Method 1: Set up an equation to find the percent. p  220 = 88 Set up an equation. p = 0.4 0.4 is 40%. So 88 is 40% of 220. Course 3 8-2 Finding Percents 88 220 p = Solve for p.
35. 35. B. Eddie weighs 160 lb, and his bones weigh 24 lb. Find the percent of his weight that his bones are. Additional Example 1B: Finding the Percent One Number Is of Another Think: What number is to 100 as 24 is to 160? Set up a proportion. Substitute. n  160 = 100  24 160 n = 2400 Find the cross products. Method 2: Set up a proportion to find the percent. Course 3 8-2 Finding Percents = number 100 part whole n 100 24 160 =
36. 36. Additional Example 1 Continued n = 15 The proportion is reasonable. Solve for n. So 15% of Eddie’s weight is bone. Course 3 8-2 Finding Percents = 15 100 24 160 160 2400 n =
37. 37. Try This : Example 1A A. What percent of 110 is 11? Insert Lesson Title Here Method 1: Set up an equation to find the percent. p  110 = 11 Set up an equation. p = 0.1 0.1 is 10%. So 11 is 10% of 110. Course 3 8-2 Finding Percents 11 110 p = Solve for p.
38. 38. B. Jamie weighs 140 lb, and his bones weigh 21 lb. Find the percent of his weight that his bones are. Think: What number is to 100 as 21 is to 140? Set up a proportion. Substitute. n  140 = 100  21 140 n = 2100 Find the cross products. Try This : Example 1B Method 2: Set up a proportion to find the percent. Course 3 8-2 Finding Percents = number 100 part whole n 100 21 140 =
39. 39. n = 15 The proportion is reasonable. Solve for n. So 15% of Jamie’s weight is bone. Course 3 8-2 Finding Percents 140 2100 n = = 15 100 21 140
40. 40. Additional Example 2A: Finding a Percent of a Number Choose a method: Set up an equation. Course 3 8-2 Finding Percents A. After a drought, a reservoir had only 66 % of the average amount of water. If the average amount of water is 57,000,000 gallons, how much water was in the reservoir after the drought? 2 3 Think: What number is 66 % of 57,000,000? 2 3 w = 66 %  57,000,000 Set up an equation. 2 3 w =  57,000,000 66 % is equivalent to . 2 3 2 3 2 3
41. 41. Additional Example 2A Continued The reservoir contained 38,000,000 gallons of water after the drought. Course 3 8-2 Finding Percents w = = 38,000,000 114,000,000 3
42. 42. Additional Example 2B: Finding Percents B. Ms. Chang deposited \$550 in the bank. Four years later her account held 110% of the original amount. How much money did Ms. Chang have in the bank at the end of the four years? Choose a method: Set up a proportion. 110  550 = 100  a Find the cross products. 60,500 = 100 a Course 3 8-2 Finding Percents = 110 100 a 550 Set up a proportion.
43. 43. Additional Example 2B Continued 605 = a Solve for a. Ms. Chang had \$605 in the bank at the end of the four years. Course 3 8-2 Finding Percents
44. 44. Try This : Example 2A Choose a method: Set up an equation. Course 3 8-2 Finding Percents A. After a drought, a river had only 50 % of the average amount of water flow. If the average amount of water flow is 60,000,000 gallons per day, how much water was flowing in the river after the drought? 2 3 Think: What number is 50 % of 60,000,000? 2 3 w = 50 %  60,000,000 Set up an equation. 2 3 w = 0.506  60,000,000 50 % is equivalent to 0.506. 2 3
45. 45. Try This : Example 2A The water flow in the river was 30,400,000 gallons per day after the drought. w = 30,400,000 Course 3 8-2 Finding Percents
46. 46. Try This : Example 2B B. Mr. Downing deposited \$770 in the bank. Four years later her account held 120% of the original amount. How much money did Mr. Downing have in the bank at the end of the four years? Choose a method: Set up a proportion. 120  770 = 100  a Find the cross products. 92,400 = 100 a Course 3 8-2 Finding Percents = 120 100 a 770 Set up a proportion.
47. 47. Try This : Example 2B Continued 924 = a Solve for a. Mr. Downing had \$924 in the bank at the end of the four years. Course 3 8-2 Finding Percents
48. 48. Lesson Quiz Find each percent to the nearest tenth. 1. What percent of 33 is 22? 2. What percent of 300 is 120? 3. 18 is what percent of 25? 4. The volume of Lake Superior is 2900 mi 3 and the volume of Lake Erie is 116 mi 3 . What percent of the volume of Lake Superior is the volume of Lake Erie? 40% 66.7% Insert Lesson Title Here 72% 4% Course 3 8-2 Finding Percents
49. 49. Warm Up Problem of the Day Lesson Presentation 8-3 Finding a Number When the Percent Is Known Course 3
50. 50. 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% Course 3 8-3 Finding a Number When the Percent Is Known 33 1 3 %
51. 51. 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 Course 3 8-3 Finding a Number When the Percent Is Known
52. 52. Learn to find a number when the percent is known. Course 3 8-3 Finding a Number When the Percent Is Known
53. 53. The Pacific giant squid can grow to a weight of 2000 pounds. This is 1250% of the maximum weight of the Pacific giant octopus. When one number is known, and is relationship to another number is given by a percent, the other number can be found. Course 3 8-3 Finding a Number When the Percent Is Known
54. 54. 60 = 0.12 n 60 is 12% of what number? Additional Example 1: Finding a Number When the Percent Is Known Set up an equation to find the number. 60 = 12%  n Divide both sides by 0.12. 500 = n 60 is 12% of 500. Set up an equation. = n 60 0.12 0.12 0.12 Course 3 8-3 Finding a Number When the Percent Is Known 12 100 12% =
55. 55. 75 = 0.25 n 75 is 25% of what number? Try This : Example 1 Set up an equation to find the number. 75 = 25%  n Divide both sides by 0.25. 300 = n 75 is 25% of 300. Set up an equation. = n 75 0.25 0.25 0.25 Course 3 8-3 Finding a Number When the Percent Is Known 25 100 25% =
56. 56. 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. Course 3 8-3 Finding a Number When the Percent Is Known
57. 57. Additional Example 2 Continued There were 20 questions on the test. 85  n = 100  17 Find the cross products. 85 n = 1700 n = 20 Course 3 8-3 Finding a Number When the Percent Is Known n = Solve for n. 1700 85
58. 58. Try This : Example 2 Choose a method : Set up a proportion to find the number. 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? Course 3 8-3 Finding a Number When the Percent Is Known = 80 100 20 n Set up a proportion.
59. 59. Try This : Example 2 Continued There were 25 questions on the test. 80  n = 100  20 Find the cross products. 80 n = 2000 n = 25 Course 3 8-3 Finding a Number When the Percent Is Known n = Solve for n. 2000 80
60. 60. 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? Additional Example 3A: 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. Course 3 8-3 Finding a Number When the Percent Is Known
61. 61. Additional Example 3A 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 Solve for n. 11.5 0.70 n = Course 3 8-3 Finding a Number When the Percent Is Known
62. 62. 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? Additional Example 3B: 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. Course 3 8-3 Finding a Number When the Percent Is Known
63. 63. Additional Example 3B Continued 55 h = 520 This giraffe will be approximately 9.5 feet tall when full grown. 55  h = 100  5.2 Find the cross products. h  9.5 520 55 h = Solve for h. Course 3 8-3 Finding a Number When the Percent Is Known
64. 64. 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? Try This : 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. Course 3 8-3 Finding a Number When the Percent Is Known
65. 65. Try This : 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 Solve for n. 15.5 0.85 n = Course 3 8-3 Finding a Number When the Percent Is Known
66. 66. B. 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? Try This : 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. Course 3 8-3 Finding a Number When the Percent Is Known
67. 67. 85 w = 12000 Bart weighs approximately 141.2 lbs. 85  w = 100  120 Find the cross products. w  141.2 Try This : Example 3 Continued 12000 85 w = Solve for h. Course 3 8-3 Finding a Number When the Percent Is Known
68. 68. You have now seen all three types of percent problems. Course 3 8-3 Finding a Number When the Percent Is Known 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 Three Types of Percent Problems
69. 69. 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 Insert Lesson Title Here 25 50 60 1 2 Course 3 8-3 Finding a Number When the Percent Is Known
70. 70. Warm Up Problem of the Day Lesson Presentation 8-4 Percent Increase and Decrease Course 3
71. 71. Warm Up 1. 14,000 is 2 % of what number? 2. 39 is 13% of what number? 3. 37 % of what number is 12? 4. 150% of what number is 189? 560,000 300 32 126 Course 3 8-4 Percent Increase and Decrease 1 2 1 2
72. 72. Problem of the Day In a school survey, 45% of the students said orange juice was their favorite juice, 25% preferred apple, and 10% preferred grapefruit. The remaining 32 students preferred grape juice. How many students participated in the survey? 160 students Course 3 8-4 Percent Increase and Decrease
73. 73. Learn to find percent increase and decrease. Course 3 8-4 Percent Increase and Decrease
74. 74. Vocabulary percent change percent increase percent decrease Insert Lesson Title Here Course 3 8-4 Percent Increase and Decrease
75. 75. Percents can be used to describe a change. Percent change is the ratio of the amount of change to the original amount. Percent increase describes how much the original amount increases. Percent decrease describes how much the original amount decreases. Course 3 8-4 Percent Increase and Decrease amount of change original amount percent change =
76. 76. Find the percent increase or decrease from 16 to 12. Additional Example 1: Percent Increase and Decrease This is percent decrease. 16 – 12 = 4 First find the amount of change. Think: What percent is 4 of 16? Set up the ratio. Course 3 8-4 Percent Increase and Decrease amount of decrease original amount 4 16
77. 77. Additional Example 1 Continued = 25% Write as a percent. = 0.25 Find the decimal form. From 16 to 12 is a 25% decrease. Course 3 8-4 Percent Increase and Decrease 4 16
78. 78. Find the percent increase or decrease from 15 to 20. Try This : Example 1 This is percent increase. 20 – 15 = 5 First find the amount of change. Think: What percent is 5 of 20? Set up the ratio. Course 3 8-4 Percent Increase and Decrease amount of increase original amount 5 20
79. 79. Try This : Example 1 Continued = 25% Write as a percent. = 0.25 Find the decimal form. From 15 to 20 is a 25% increase. Course 3 8-4 Percent Increase and Decrease 5 20
80. 80. A. When Jim was exercising, his heart rate went from 70 beats per minute to 98 beats per minute. What was the percent increase? Additional Example 2: Life Science Application Think: What percent is 28 of 70? Set up the ratio. 98 – 70 = 28 First find the amount of change. Course 3 8-4 Percent Increase and Decrease 28 70 amount of increase original amount
81. 81. Additional Example 2 Continued = 40% Write as a percent. Jim’s heart rate increased by 40% when he exercised. Course 3 8-4 Percent Increase and Decrease = 0.4 Find the decimal form. 70 28
82. 82. B. In 1999, a certain stock was worth \$1.25 a share. In 2002, the same stock was worth \$0.85 a share. What was the percent decrease? Additional Example 2B: Application 1.25 – 0.85 = 0.40 First find the amount of change. Think: What percent is 0.40 of 1.25? Set up the ratio. Course 3 8-4 Percent Increase and Decrease amount of decrease original amount 1.25 0.40
83. 83. Additional Example 2B Continued = 32% Write as a percent. = 0.32 Find the decimal form. The value of the stock decreased by 32%. Course 3 8-4 Percent Increase and Decrease 1.25 0.40
84. 84. A. When Jeff was watching TV, the number of times his eyelids blinked went from 50 blinks per minute to 75 blinks per minute. What was the percent increase? Try This : Example 2A Think: What percent is 25 of 50? Set up the ratio. 75 – 50 = 25 First find the amount of change. Course 3 8-4 Percent Increase and Decrease 25 50 amount of increase original amount
85. 85. = 50% Write as a percent. The blinking of Jeff’s eyelids increased by 50% when he watched TV. Try This : Example 2A Continued Course 3 8-4 Percent Increase and Decrease = 0.5 Find the decimal form. 50 25
86. 86. B. In 2000, a certain stock was worth \$9.00 a share. In 2003, the same stock was worth \$3.80 a share. What was the percent decrease? Try This: Example 2B 9.00 – 3.80 = 5.20 First find the amount of change. Think: What percent is 5.20 of 9.00? Set up the ratio. Course 3 8-4 Percent Increase and Decrease amount of decrease original amount 9.00 5.20
87. 87. The value of the stock decreased by about 57.8%. Try This: Example 2B Continued Course 3 8-4 Percent Increase and Decrease 9.00 5.20 = 0.57 Find the decimal form. = 57.7% Write as a percent.
88. 88. A. Sarah bought a DVD player originally priced at \$450 that was on sale for 20% off. What was the sale price? Additional Example 3A: Percent Increase and Decrease \$450  20% First find 20% of \$450. \$450  0.20 = \$90 20% = 0.20 The amount of decrease is \$90. Think: The reduced price is \$90 less than \$450. \$450 – \$90 = \$360 Subtract the amount of decrease. The sale price of the DVD player was \$360. Course 3 8-4 Percent Increase and Decrease
89. 89. B. Mr. Olsen has a computer business in which he sells everything at 40% above the wholesale price. If he purchased a printer for \$85 wholesale, what will be the retail price? Additional Example 3B: Percent Increase and Decrease \$85  40% First find 40% of \$85. \$85  0.40 = \$34 40% = 0.40 The amount of increase is \$34. Think: The retail price is \$34 more than \$85. \$85 + \$34 = \$119 Add the amount of increase. The retail price of this printer will be \$119. Course 3 8-4 Percent Increase and Decrease
90. 90. A. Lily bought a dog house originally priced at \$750 that was on sale for 10% off. What was the sale price? Try This : Example 3A \$750  10% First find 10% of \$750. \$750  0.10 = \$75 10% = 0.10 The amount of decrease is \$75. Think: The reduced price is \$75 less than \$750. \$750 – \$75 = \$675 Subtract the amount of decrease. The sale price of the dog house was \$675. Course 3 8-4 Percent Increase and Decrease
91. 91. B. Barb has a grocery store in which she sells everything at 50% above the wholesale price. If she purchased a prime rib for \$30 wholesale, what will be the retail price? \$30  50% First find 50% of \$30. \$30  0.50 = \$15 50% = 0.50 The amount of increase is \$15. Think: The retail price is \$15 more than \$30. \$30 + \$15 = \$45 Add the amount of increase. The retail price of the prime rib will be \$45. Try This : Example 3B Course 3 8-4 Percent Increase and Decrease
92. 92. Lesson Quiz Find each percent increase or decrease to the nearest percent. 1. from 12 to 15 2. from 1625 to 1400 3. from 37 to 125 4. from 1.25 to 0.85 5. A computer game originally sold for \$40 but is now on sale for 30% off. What is the sale price of the computer game? 14% decrease 25% increase Insert Lesson Title Here 238% increase 32% decrease \$28 Course 3 8-4 Percent Increase and Decrease
93. 93. Warm Up Problem of the Day Lesson Presentation 8-6 Applications of Percents Course 3
94. 94. Warm Up Estimate. 1. 20% of 602 2. 133 out of 264 3. 151% of 78 4. 0.28 out of 0.95 120 50% 120 30% Possible answers: Course 3 8-6 Applications of Percents
95. 95. Problem of the Day What is the percent discount on a purchase of three shirts if you take advantage of the shirt sale? All Shirts on Sale! Buy 2—Get the Third for Half Price! Course 3 8-6 Applications of Percents 16 % 2 3
96. 96. Learn to find commission, sales tax, and withholding tax. Course 3 8-6 Applications of Percents
97. 97. Vocabulary commission commission rate sales tax withholding tax Insert Lesson Title Here Course 3 8-6 Applications of Percents
98. 98. Real estate agents often work for commission . A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate . Often agents are paid a commission plus a regular salary. The total pay is a percent of the sales they make plus a salary. commission rate  sales = commission Course 3 8-6 Applications of Percents
99. 99. A real-estate agent is paid a monthly salary of \$900 plus commission. Last month he sold one condominium for \$65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month? Additional Example 1: Multiplying by Percents to Find Commission Amounts First find his commission. 4%  \$65,000 = c commission rate  sales = commission Course 3 8-6 Applications of Percents
100. 100. 0.04  65,000 = c Change the percent to a decimal. Additional Example 1 Continued 2600 = c Solve for c. He earned a commission of \$2600 on the sale. Now find his total pay for last month. \$2600 + \$900 = \$3500 commission + salary = total pay His total pay for last month was \$3500. Course 3 8-6 Applications of Percents
101. 101. A car sales agent is paid a monthly salary of \$700 plus commission. Last month she sold one sports car for \$50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month? Try This : Example 1 First find her commission. 5%  \$50,000 = c commission rate  sales = commission Course 3 8-6 Applications of Percents
102. 102. 0.05  50,000 = c Change the percent to a decimal. Try This : Example 1 Continued 2500 = c Solve for c. The agent earned a commission of \$2500 on the sale. Now find her total pay for last month. \$2500 + \$700 = \$3200 commission + salary = total pay Her total pay for last month was \$3200. Course 3 8-6 Applications of Percents
103. 103. Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller. Course 3 8-6 Applications of Percents
104. 104. If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at \$16.99 each and one DVD for \$36.29? Additional Example 2: Multiplying by Percents to Find Sales Tax Amounts \$70.27 Total Price 0.0675  70.27 = 4.743225 Convert tax rate to a decimal and multiply by the total price. Adrian would pay \$4.74 in sales tax. Course 3 8-6 Applications of Percents CD: 2 at \$16.99 \$33.98 DVD: 1 at \$36.29 \$36.29
105. 105. Try This : Example 2 Amy rents a hotel for \$45 per night. She rents for two nights and pays a sales tax of 13%. How much tax did she pay? Insert Lesson Title Here \$45  2 = \$90 Find the total price for the hotel stay. \$90  0.13 = \$11.70 Convert tax rate to a decimal and multiply by the total price. Amy spent \$11.70 on sales tax. Course 3 8-6 Applications of Percents
106. 106. A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax . Course 3 8-6 Applications of Percents
107. 107. Anna earns \$1500 monthly. Of that, \$114.75 is withheld for Social Security and Medicare. What percent of Anna’s earnings are withheld for Social Security and Medicare? Additional Example 3: Using Proportions to Find the Percent of Tax Withheld Think: What percent of \$1500 is \$114.75? Solve by proportion: n  1500 = 100  114.75 Find the cross products. Course 3 8-6 Applications of Percents 114.75 1500 n 100 =
108. 108. Additional Example 3 Continued n = 7.65 7.65% of Anna’s earnings is withheld for Social Security and Medicare. 1500 n = 11,475 Divide both sides by 1500. Course 3 8-6 Applications of Percents 11,475 1500 n =
109. 109. BJ earns \$2500 monthly. Of that, \$500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax? Try This : Example 3 Think: What percent of \$2500 is \$500? Solve by proportion: n  2500 = 100  500 Find the cross products. Course 3 8-6 Applications of Percents 500 2500 n 100 =
110. 110. Try This : Example 3 Continued n = 20 20% of BJ’s earnings are withheld for income tax. 2500 n = 50,000 Divide both sides by 2500. Course 3 8-6 Applications of Percents 50000 2500 n =
111. 111. A furniture sales associate earned \$960 in commission in May. If his commission is 12% of sales, how much were his sales in May? Additional Example 4: Dividing by Percents to Find Total Sales Think: \$960 is 12% of what number? Solve by equation: 960 = 0.12  s Let s = total sales. The associate’s sales in May were \$8000. Course 3 8-6 Applications of Percents 960 0.12 = s Divide each side by 0.12.
112. 112. A sales associate earned \$770 in commission in May. If his commission is 7% of sales, how much were his sales in May? Try This : Example 4 Think: \$770 is 7% of what number? Solve by equation: 770 = 0.07  s Let s represent total sales. The associate’s sales in May were \$11,000. Course 3 8-6 Applications of Percents 770 0.07 = s Divide each side by 0.07.
113. 113. Lesson Quiz: Part 1 1. The lunch bill was \$8, and you want to leave a 15% tip. How much should you tip? 2. The sales tax is 5.75%, and the shirt costs \$20. What is the total cost of the shirt? 3. As of 2001, the minimum hourly wage was \$5.15. Congress proposed to increase it to \$6.15 per hour. To the nearest percent, what is the proposed percent increase in the minimum wage? \$21.15 \$1.20 Insert Lesson Title Here 19% Course 3 8-6 Applications of Percents
114. 114. Lesson Quiz: Part 2 4. It costs a business \$13.30 to make its product. To satisfy investors, the company needs to make \$4 profit per unit. To the nearest percent, what should be the company’s markup? Insert Lesson Title Here 30% Course 3 8-6 Applications of Percents
115. 115. Warm Up Problem of the Day Lesson Presentation 8-7 More Applications of Percents Course 3
116. 116. Warm Up 1. What is 35 increased by 8%? 2. What is the percent of decrease from 144 to 120? 3. What is 1500 decreased by 75%? 4. What is the percent of increase from 0.32 to 0.64? 37.8 375 100% Course 3 8-7 More Applications of Percents 16 % 2 3
117. 117. Problem of the Day Maggie is running for class president. A poll revealed that 40% of her classmates have decided to vote for her, 32% have decided to vote for her opponent, and 7 voters are undecided. If she needs 50% of the vote to win, how many of the undecided voters must vote for Maggie for her to win the election? 3 Course 3 8-7 More Applications of Percents
118. 118. Learn to compute simple interest. Course 3 8-7 More Applications of Percents
119. 119. Vocabulary interest simple interest principal rate of interest Insert Lesson Title Here Course 3 8-7 More Applications of Percents
120. 120. When you borrow money from a bank, you pay interest for the use of the bank’s money. When you deposit money into a savings account, you are paid interest. Simple interest is one type of fee paid for the use of money. I = P  r  t Course 3 8-7 More Applications of Percents Simple Interest Principal is the amount of money borrowed or invested Rate of interest is the percent charged or earned Time that the money is borrowed or invested (in years)
121. 121. To buy a car, Jessica borrowed \$15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay? Additional Example 1: Finding Interest and Total Payment on a Loan First, find the interest she will pay. I = P  r  t Use the formula. I = 15,000  0.09  3 Substitute. Use 0.09 for 9%. <ul><ul><li>I = 4050 Solve for I. </li></ul></ul>Course 3 8-7 More Applications of Percents
122. 122. Additional Example 1 Continued Jessica will pay \$4050 in interest. P + I = A principal + interest = amount 15,000 + 4050 = A Substitute. <ul><ul><li>19,050 = A Solve for A. </li></ul></ul>You can find the total amount A to be repaid on a loan by adding the principal P to the interest I . Jessica will repay a total of \$19,050 on her loan. Course 3 8-7 More Applications of Percents
123. 123. To buy a laptop computer, Elaine borrowed \$2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay? Try This : Example 1 First, find the interest she will pay. I = P  r  t Use the formula. I = 2,000  0.05  3 Substitute. Use 0.05 for 5%. <ul><ul><li>I = 300 Solve for I. </li></ul></ul>Course 3 8-7 More Applications of Percents
124. 124. Try This : Example 1 Continued Elaine will pay \$300 in interest. P + I = A principal + interest = amount 2000 + 300 = A Substitute. <ul><ul><li>2300 = A Solve for A. </li></ul></ul>You can find the total amount A to be repaid on a loan by adding the principal P to the interest I . Elaine will repay a total of \$2300 on her loan. Course 3 8-7 More Applications of Percents
125. 125. Additional Example 2: Determining the Amount of Investment Time I = P  r  t Use the formula. 450 = 6,000  0.03  t Substitute values into the equation. <ul><ul><li>2.5 = t Solve for t. </li></ul></ul>Nancy invested \$6000 in a bond at a yearly rate of 3%. She earned \$450 in interest. How long was the money invested? 450 = 180 t The money was invested for 2.5 years, or 2 years and 6 months. Course 3 8-7 More Applications of Percents
126. 126. Try This : Example 2 I = P  r  t Use the formula. 200 = 4,000  0.02  t Substitute values into the equation. <ul><ul><li>2.5 = t Solve for t . </li></ul></ul>TJ invested \$4000 in a bond at a yearly rate of 2%. He earned \$200 in interest. How long was the money invested? 200 = 80t The money was invested for 2.5 years, or 2 years and 6 months. Course 3 8-7 More Applications of Percents
127. 127. I = P  r  t Use the formula. I = 1000  0.0325  18 Substitute. Use 0.0325 for 3.25%. <ul><ul><li>I = 585 Solve for I . </li></ul></ul>Now you can find the total. Additional Example 3: Computing Total Savings John’s parents deposited \$1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3.25%? Course 3 8-7 More Applications of Percents
128. 128. P + I = A Use the formula. 1000 + 585 = A <ul><ul><li>1585 = A </li></ul></ul>John will have \$1585 in the account after 18 years. Additional Example 3 Continued Course 3 8-7 More Applications of Percents
129. 129. I = P  r  t Use the formula. I = 1000  0.075  50 Substitute. Use 0.075 for 7.5%. <ul><ul><li>I = 3750 Solve for I. </li></ul></ul>Now you can find the total. Try This : Example 3 Bertha deposited \$1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%? Course 3 8-7 More Applications of Percents
130. 130. P + I = A Use the formula. 1000 + 3750 = A <ul><ul><li>4750 = A </li></ul></ul>Bertha will have \$4750 in the account after 50 years. Try This : Example 3 Continued Course 3 8-7 More Applications of Percents
131. 131. Mr. Johnson borrowed \$8000 for 4 years to make home improvements. If he repaid a total of \$10,320, at what interest rate did he borrow the money? Additional Example 4: Finding the Rate of Interest P + I = A Use the formula. 8000 + I = 10,320 I = 10,320 – 8000 = 2320 Find the amount of interest. He paid \$2320 in interest. Use the amount of interest to find the interest rate. Course 3 8-7 More Applications of Percents
132. 132. Additional Example 4 Continued 2320 = 32,000  r Multiply. I = P  r  t Use the formula. 2320 = 8000  r  4 Substitute. 0.0725 = r Course 3 8-7 More Applications of Percents 2320 32,000 = r Divide both sides by 32,000. Mr. Johnson borrowed the money at an annual rate of 7.25%, or 7 %. 1 4
133. 133. Mr. Mogi borrowed \$9000 for 10 years to make home improvements. If he repaid a total of \$20,000 at what interest rate did he borrow the money? Try This : Example 4 P + I = A Use the formula. 9000 + I = 20,000 I = 20,000 – 9000 = 11,000 Find the amount of interest. He paid \$11,000 in interest. Use the amount of interest to find the interest rate. Course 3 8-7 More Applications of Percents
134. 134. Try This : Example 4 Continued 11,000 = 90,000  r Multiply. I = P  r  t Use the formula. 11,000 = 9000  r  10 Substitute. Mr. Mogi borrowed the money at an annual rate of about 12.2%. Course 3 8-7 More Applications of Percents 11,000 90,000 = r Divide both sides by 90,000. 0.12 = r
135. 135. Lesson Quiz: Part 1 1. A bank is offering 2.5% simple interest on a savings account. If you deposit \$5000, how much interest will you earn in one year? 2. Joshua borrowed \$1000 from his friend and paid him back \$1050 in six months. What simple annual interest did Joshua pay his friend? 10% \$125 Insert Lesson Title Here Course 3 8-7 More Applications of Percents
136. 136. Lesson Quiz: Part 2 3. The Hemmings borrowed \$3000 for home improvements. They repaid the loan and \$600 in simple interest four years later. What simple annual interest rate did they pay? 4. Mr. Berry had \$120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years? Insert Lesson Title Here 5% \$171,000 Course 3 8-7 More Applications of Percents