February 6
Name:
Problems 1 - 4 : Choose the best answer to each of the following questions. Explain your
reasoning with one or more complete sentences.
1. (3 pts) Suppose the value of college tuition changed by 4% over the past ten years.
This means that
c. tuition increased in value over the past ten years.
A relative change that is positive over time is an increase.
2. (3 pts) Your receipt shows that you paid $41.88 for a new shirt, including sales tax.
The sales tax rate is 4.7% . The amount you paid in sales tax was
c. $41.88 −
$41.88
1.047
$41.88 = (100% + 4.7%) × Price, but the amount paid in tax is 4.7% × Price. The
price is $41.88/1.047.
3. (3 pts) You currently earn $1000 per month, but you are expecting your earnings to
rise 10% per year. This means that in five years you expect to be earning
c. somewhat more than $1500 per month.
Each year 10% is added from the previous year. The first year is $1100 per month,
the next is $1210 per month, etc.
4. (3 pts) The number 70,000 is the same as
a. 7 × 104
104 = 10, 000.
Problems 5 - 6: Decide whether each of the following statements make sense (or is
clearly true) or does not make sense (or is clearly false). Explain your reasoning.
5. (2 pts) I’ve decreased my caloric intake by 125%, which as helped me lose weight.
False. Decreasing by 125% results in a negative intake. For instance, 125% of 2000
calories is 2500 calories. The intake is -500 calories. That does not make sense.
6. (2 pts) If they raise taxes by 10% every year, in a decade we’ll be paying everything
we earn to taxes.
False.You must take percents of percents.
7. (2 pts) Express the first number as a percentage of the second number. The median
salary for U.S. men aged 25 to 34 in 2009 was $49,105 and the median salary for U.S.
women aged 25 to 34 in 2009 was $ 47,260 (census.gov).
$49105
= 1.039, or 103.9%
$47260
8. (4 pts) Find the absolute change and the relative change in the following case. The
number of daily newspapers in the United States was 2226 in 1900 and 1420 in 2010.
The reference number is 2226 newspapers. Absolute change = 1420 − 2226 = −806
papers. Relative change = −806/2226 = −0.362, or − 36.2%.
9. (2 pts) Solve. Simon’s monthly take-home pay (after taxes) is $2200. If he pays 21%
of his gross pay (before taxes) in tax, what is his gross pay?
$2200 = (100% − 21%) × Gross, so Gross = $2200/0.79 = $2784.81.
10. (3 pts) Use estimation to make the following comparisons. Discuss your conclusion.
Which is greater: the time you spend in a year studying or the time you spend in a
year sleeping?
Estimate with numbers. Answers may vary. Sleep 7 hours / day, 365 days / year
= 2555 hours / year. Study 20 hours / week, 35 weeks / year = 245 hours / year.
More hours are spend sleeping.
11. Bonus 2 pts: This is an example taken from The New York Times. It is
extra credit and optional.
Find the absolute difference and the relative difference in the following case. A community college’s tuition and fees in Tennessee is about $3,800 and the national average
is about $3,300.
Refence number is $3,300. Absolute difference = $3800 − $3300 = $500. Relative
difference = $500/$3300 = 0.151 or 15.1%