Math 2000 - Solutions 4
Fall 2001
Unit 3A 22. The area of Norway is 24% more than the area of Colorado, so Norway's area is (100% + 24%) = 124% of Colorado's area. 30. We must use percentage points (p.p.). The absolute change between the 1970 (old) and 1996 (new) percentages of the population living in developed countries is 20 p.p. - 27 p.p. = -7 p.p.; this is a 7 percentage point drop. In relative terms, the difference is $-\frac{7}{27} = 0.2593$, which is a 25.93% drop. Thus the percentage of the population living in developed countries decreased by about 7 percentage points or 26%. 36. The sentence that describes the situation is
Pre-tax cost + (6.2% of pre-tax cost) = $107.69.
Simplifying this sentence, we have
106.2% $\times$ pre-tax cost = $107.69 or 1.062 $\times$ pre-tax cost = $107.69.
Dividing both sides of the sentence by 1.062, we find that the pre-tax cost is $\frac{\$107.69}{1.062} = \$101.40$ 48. Notice that the quantity that is changing is itself a percentage, so we should refer to percentage points (p.p). The sentence that describes the change is
Last winter + (16% of last winter) = 80 p.p.
where last winter refers to the percentage of people who said they are not worried last winter. As done in class, we can now write this sentence as
116% $\times$ Last winter = 80 p.p. or 1.16 $\times$ Last winter = 80 p.p.
Dividing both sides of the sentence by 1.16, we find that the percentage of people who said they are not worried last winter is $\frac{80}{1.16}= 69\%$. 50. False. Your final salary is (0.95)(1.05) = 0.9975 times--or 99.75% of--your original salary, which is less than your original salary. For example, if your salary started at $100, after the pay cut it would be $95. After the pay raise, it would be $99.75. 62. False; bald men comprise $(0.20)(0.40)=0.08=8\%$ of the class. Unit 3B 2b. $1.5 \times 10^9 = 1,500,000,000 = 1.5$ billion. 4e. $250\ {\rm million} = 250,000,000 = 2.5 \times 10^{8}$. 6a. $(8 \times 10^{12})/(4 \times 10^9) = (8/4) \times (10^{12} / 10^9) = 2 \times 10^3$.