Lab 5
More Percentage Problems
2. Poverty: Good News or Bad News? According to Census Bureau figures, in 1990
13.1% of the U.S. population lived in poverty, while only 12.4% of the population lived in
poverty in 2000. Assume populations of 249 million and 281 million in 1990 and 2000,
respectively.
a. Did the actual number of people living in poverty increase or decrease between
1990 and 2000? Show your work.
=.131*249=32.6
= .124*281=34.8
b. Is the news about poverty good or bad? Justify your answer.
3. Video Store:
At the local Video Station, you pay a total of
$15.50 for a DVD, after tax had been added.
Assuming a local sales tax of 7.5%, what is the
retail (before-tax) price of the DVD? [Hint: To
solve this, think about the price you paid as 100%
of the retail price plus 7.5% of the retail price for
tax.]
15.50/x = 107.5/100
15.50/x = 1.075
15.50 = 1.075*x
15.50/107.5 = x
14.42
4. Obesity in American Kids: A study that appeared in the Journal of the American
Medical Association (December 12, 2001) reports on obesity American Children.
According to the study, the percentage of overweight black and Hispanic children "more
than doubled" between 1986 and 1998; the percentage of overweight white children
increased by 50%. [percentage change] Specifically, in 1986 the percentage of
overweight 4-12-year olds was 8%, 10%, and 8% for black, Hispanic, and white
children, respectively. [part/whole] In 1998, the percentages had risen to 22%, 22%,
and 12%, respectively. [part/whole] Among the reasons given for the increases were
increased television watching, increased us of computers and video games, and more
reliance on fast food. The study was based on data from the National Longitudinal
Survey of Youth, which followed a sample of 8270 children from 1986 to 1998.
a. What types of percentages were used in this article: percent of, percent
change, percent more or less than? See annotations above.
b. The article says that the percentage of overweight black and Hispanic
children "more than doubled" between 1986 and 1998. "Double" represents what
percent increase? 100%
c. Given the figures in this summary, is it true that the percentage of
overweight white children increased by 50% between 1986 and 1998? Yes, it is
true. Show calculations to confirm or deny. (.12-.08)/.08 = .5 . . .
d. If the percentage of overweight white children increased by 50%, can you
conclude that the number of overweight white children increased by 50%
between 1986 and 1998? Why or why not? No, you cannot conclude so,
because the base (the number of white children) most likely changed.
The number of white 4-12 year olds in 1998 was 23 million which is 17 %
larger than the number of such children in 1986. How many white 4-12 year
olds were there in 1986?
23/x = 117/100
23/x = 1.17
19 1.17 *x
23/1.17 = x
19.7 million
f. Calculate the number of overweight white children in 1986 and 1998. What
was the percent increase in the number of overweight white children from 1986
to 1998?
=.12*23 = 2.76 million overweight white children in 1998
= .08 * 19.7 = 1.58 million in 1986
100 * (2.76-19.7)/19.7 = 74.7% increase
g. Can the rates of increase in the percentage of the population that is
overweight continue indefinitely? Discuss how long these increases could
reasonably continue.
The basic answer is that it cannot. Eventually (actually, quite soon)
the number of obese children would be greater than the number of
children. We will examine why in the second half of the class.