Unit 3A

Unit 3A

Uses and Abuses

of Percentages

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

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%

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.

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