Unit 3A

Unit 3A

Uses and Abuses

of Percentages

Fill in the Blanks

Find the absolute change and the relative change in the following cases.

45. The number of refugees in the world increased from 8.7 ­million in 2005 to 16.1 million in 2015.

Find the absolute change

45. The number of refugees in the world increased from 8.7 ­million in 2005 to 16.1 million in 2015.

16.1 million - 8.7 million = 7.4 million

Fill in the Blanks

Find the absolute change and the relative change in the following cases.

45. The number of refugees in the world increased from 8.7 ­million in 2005 to 16.1 million in 2015.

Find the relative change.

45. The number of refugees in the world increased from 8.7 ­million in 2005 to 16.1 million in 2015.

16.1 million - 8.7 million = 7.4 million

 $\frac{new-old}{old}=\frac{16.1\ million\ -8.7\ million}{8.7\ million}=\frac{7.4\ million}{8.7\ million}\approx0.85057$      

about 85.06%

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Find the absolute change and the relative change in the following cases.

47. The U.S. per capita consumption of beef decreased from 67.8 pounds in 2000 to 55.4 pounds in 2016.

Fill in the Blanks

Find the absolute change and the relative change in the following cases.

47. The U.S. per capita consumption of beef decreased from 67.8 pounds in 2000 to 55.4 pounds in 2016.

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49. The life expectancy (at birth) of American women (81.2 years) is

percent greater than the life ­expectancy of men (76.4 years).

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51. In 2015, the median age at first marriage of U.S. women (27.1 years) was

percent less than the median age at first marriage of U.S. men (29.2 years).

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53. The population of Michigan is 63% greater than the population of Missouri, so Michigan’s population is

% of Missouri’s population.

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55. The population of Hawaii is 52% less than the population of Arkansas, so the population of Hawaii is

% of the population of Arkansas.

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57. The wholesale price of a toaster is 30% less than the retail price. Therefore, the wholesale price is

times the retail price.

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59. The original retail price of a TV is 20% more than its on-sale price. Therefore, the retail price is

times the on-sale price.

Fill in the Blanks

Describe each of the following changes in two ways: as an absolute change in terms of percentage points and as a relative change in terms of a percentage.

61. The percentage of Republicans in the House of Representatives increased from 40.9% in 2010 to 55.3% in 2016.

Fill in the Blanks

Describe each of the following changes in two ways: as an absolute change in terms of percentage points and as a relative change in terms of a percentage.

61. The percentage of Republicans in the House of Representatives increased from 40.9% in 2010 to 55.3% in 2016.

Fill in the Blanks

Describe each of the following changes in two ways: as an absolute change in terms of percentage points and as a relative change in terms of a percentage.

63. Alcohol use by high school seniors decreased from 50.0% in 2000 to 35.3% in 2015.

Fill in the Blanks

Describe each of the following changes in two ways: as an absolute change in terms of percentage points and as a relative change in terms of a percentage.

63. Alcohol use by high school seniors decreased from 50.0% in 2000 to 35.3% in 2015.

Fill in the Blanks

67.The total (after-tax) cost of a laptop computer is $1278.24. The local sales tax rate is 7.6%. What is the retail (pre-tax) price?

67.The total (after-tax) cost of a laptop computer is $1278.24. The local sales tax rate is 7.6%. What is the retail (pre-tax) price?

1.00x + .076 x = 1278.24

1.076x=1278.24

 $x=\frac{1278.24}{1.076}$ = 1187.95553

Open Ended

71–74: Shifting Reference Value. State whether the following statements are true or false, and explain why. If a statement is false, state the true change.

71. If the national unemployment rate decreased at an annual rate of 2% per year for three consecutive years, then the rate decreased by 6% over the three-year period.

71. If the national unemployment rate decreased at an annual rate of 2% per year for three consecutive years, then the rate decreased by 6% over the three-year period.

• Pick a number, any number. (100 is a good one)

• First year 100 is down by 2% of 100 (which is 2) to 98

• Second year, the reference changes to 98 now, so we reduce by 2% of 98 (which is 1.96) to 96.04.

• Third year, we reduce 96.04 by 2% of 96.04 to 94.1192.

• This is a fraction over a 6% reduction which would be 94 even.

Open Ended

75–80: Is It Possible? Determine whether the following claims could be true. Explain your answer.

75. Anna bought a surfboard online and saved 125%.

Open Ended

75–80: Is It Possible? Determine whether the following claims could be true. Explain your answer.

77. Average hotel room rates have increased 100% in the last 20 years.

Open Ended

81. Average Percentages. Suppose you have an 80% average in a class going into the final exam. You receive a 90% grade on the final exam. In general, does it follow that your average for the entire course is 85%? Explain.

81. Suppose you have an 80% average in a class going into the final exam. You receive a 90% grade on the final exam. In general, does it follow that your average for the entire course is 85%? Explain.

Open Ended

83. Forty percent of the students at an orientation are women and 20% of the women are engineering students. Therefore, 40%×20%=8% of the students at the orientation are female engineering students.

83. Forty percent of the students at an orientation are women and 20% of the women are engineering students. Therefore, 40%×20%=8% of the students at the orientation are female engineering students.

• Pick a number. Start with 200 students.

• 40% of 200 is 80

• 20% of 80 is 16

• 16/200 is 8% might be correct, so what'd we do? operations?

• Start with any # and multiply it by 0.40 and then by 0.20.

   $\left(x\cdot0.40\right)\cdot0.20\ =\ x\left(0.40\cdot0.20\right)$  

• Is the same as muliplying by 0.08 (associativity).

Open Ended

85. Fifty percent of the cars in the rental pool have Bluetooth capability and 20% of the cars have GPS. Therefore, 50%+20%=70% of the cars have Bluetooth or GPS.

Fifty percent of the cars in the rental pool have Bluetooth capability and 20% of the cars have GPS. Therefore, 50%+20%=70% of the cars have Bluetooth or GPS.

• Total number is 100 cars.

• Bluetooth is 40+10 out of 100 or 50%

• GPS is 10 + 10 out of 100 is 20%

• But, Bluetooth and GPS is 40 + 10 + 10 which is 60, not 70%.

• The extra comes from accidentally counting the overlap twice.

Fill in the Blanks

87. The 4550 men in the arena comprised 85% of the people in the arena. How many people were in the arena?

87. The 4550 men in the arena comprised 85% of the people in the arena. How many people were in the arena?

0.85 (x) = 4550

x= 4550/0.85

x = 5352.94

or 5353 men

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88. In 2016, 84.0% of households with televisions subscribed to cable, an increase of 7.8% over 2000. What percentage of households with televisions subscribed to cable in 2000?

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89. With 2.4 million digital subscribers, Game Informer Magazine (ranked first) has 1150% more digital subscribers than National Geographic (ranked third). How many digital subscribers does National Geographic have?

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93. “The unemployment rate has risen more than a percentage point, to 8.5% in February from 7.1% last November.” What is the relative change in the unemployment rate expressed as a percentage?