Math 2000 solutions 4

Math 2000 - Solutions 4
Spring 2002

Unit 3A 22. This problem is just a matter of wording. Recall from the Of versus More Than rule on page 139, that if the area of Norway is 24% more than the area of Colorado, then Norway's area is 124% of Colorado's area. 32. This is a problem in which the changing quantity is itself a percentage; therefore, you must use percentage point to express the absolute difference. The absolute difference between the 1960s and 1990s five-year survival rate for Blacks for all forms of cancer is $44\% - 27\% = 17$ percentage points. In relative terms, the difference was

$\begin{displaymath} \frac{44\%-27\%}{27\%} = 0.6296, \end{displaymath}$

which is a 62.96% increase. 38. The sentence that describes this situation is

$\begin{displaymath} \mbox{Labeled price} + 8.1\% \mbox{ of labeled price} = \$3,706.30. \end{displaymath}$

We can rewrite this sentence as

$\begin{displaymath} (100\% + 8.1\%) \times \mbox{labeled price}= 108.1\% \times \mbox{labeled price}= \$3,706.30. \end{displaymath}$

Noting that $108.1\% = 1.081$ , we have

$\begin{displaymath} 1.081 \times \mbox{labeled price}= \$3,706.30. \end{displaymath}$

Dividing both sides of the sentence by 1.081, we find that

$\begin{displaymath} \mbox{Labeled price} = \frac{\$3706.30}{1.081} = \$3428.58. \end{displaymath}$

You should check that if you add 8.1% tax to $3428.58, the result is $3,706.30. 46. The sentence that goes with this problem is

$\begin{displaymath} \mbox{1970 work level} - 98.5\% \mbox{ of 1970 work level} = 8 \mbox{ man-days }. \end{displaymath}$

This sentence can be rewritten as

$\begin{displaymath} (100\% - 98.5\%) \times \mbox{1970 work level}= 1.5\% \times \mbox{1970 work level} = 8 \mbox{ man-days }. \end{displaymath}$

Noting that $1.5\%=0.015$ , we have

$\begin{displaymath} 0.015 \times \mbox{1970 work level} = 8 \mbox{ man-days } \end{displaymath}$

Dividing both sides of the sentence by 0.015, we see that

$\begin{displaymath} \mbox{1970 work level}= \frac{8 \mbox{ man-days }}{0.015} = 533.3 \mbox{ man-days}. \end{displaymath}$

52. False. Suppose the original test score is 1000 (you can pick any number). A 20% reduction results in a test score of $1000 - (20\% \times 1000) = 800$ . A 30% increase from 800 results in a test score of $800 + (30\% \times 800) = 1040$ . A 10% increase over 1000 would be a test score of 1100. In fact, the actual increase is only (relative difference)

$\begin{displaymath} \frac{1040-1000}{1000} = 0.04 = 4\%. \end{displaymath}$

64. True. Those who drive do not take a bus, and so (40+15)% = 55% either drive or take a bus, leaving 45% who do neither. Unit 3B 2d. $2.3 \times 10^6 = 2,300,000 =2.3$ million. 4d. $0.002 \times 10^{6} = 2,000 = 2 \times 10^{3}$ . 6b. $(7.5 \times 10^{21}) / (1.5 \times 10^{13}) = (7.5/1.5) \times (10^{21} / 10^{13}) = 5 \times 10^{8}$ .