Chapter 7.5, Problem 25E

i.

To determine

To calculate the percentof change in number of pairs of footwear from the year $1996$ to $2000$ .

Answer to Problem 25E

The percent of change in number of pairs of footwear from the year $1996$ to $2000$ is

about $50.8\%$ .

Explanation of Solution

Given information:

Consider, the graph provided in the question,

  

The pairs of footwear manufactured in the year $1996$ is $196.0\text{ millions}$ .

The pairs of footwear manufactured in the year $1997$ is $190.1\text{ millions}$ .

The pairs of footwear manufactured in the year $1998$ is $163.2\text{ millions}$ .

The pairs of footwear manufactured in the year $1999$ is $120.9\text{ millions}$ .

The pairs of footwear manufactured in the year $2000$ is $96.5\text{ millions}$ .

Formula used:

  $\text{Percent of change, }p\%=\frac{\text{Amount of increase or decrease}}{\text{Original amount}}$

Calculation:

The decrease in number of pairs of footwear from the year $1996$ to $2000$ is:

  $\begin{array}{l}=196.0-96.5\\ =99.5\text{ millions}\end{array}$

Therefore,

Percent of change in number of pairs of footwear is:

  $\begin{array}{l}p\%=\frac{99.5}{196.0}\left[\text{Substitute}\right]\\ p\%\simeq \text{0}\text{.5077}=50.8\%\left[\text{Divide}\text{. Then write decimal as a percent}\right]\end{array}$

Conclusion:

Hence,

The percent of change in number of pairs of footwear from the year $1996$ to $2000$

is about $50.8\%$ .

ii.

To determine

To compare in which year did the number of pairs of footwear decreases the most from previous year and what was the approximate percent of change.

Answer to Problem 25E

The decrease in number of pairs of footwear in the year $1999$ from the previous year is $42.3\text{ millions}$ which is maximum as compared to others and

The percent of change is about $25.9\%$ .

Explanation of Solution

Given information:

Consider, the graph provided in the question,

  

The pairs of footwear manufactured in the year $1996$ is $196.0\text{ millions}$ .

The pairs of footwear manufactured in the year $1997$ is $190.1\text{ millions}$ .

The pairs of footwear manufactured in the year $1998$ is $163.2\text{ millions}$ .

The pairs of footwear manufactured in the year $1999$ is $120.9\text{ millions}$ .

The pairs of footwear manufactured in the year $2000$ is $96.5\text{ millions}$ .

Formula used:

  $\text{Percent of change, }p\%=\frac{\text{Amount of increase or decrease}}{\text{Original amount}}$

Calculation:

The decrease in number of pairs of footwear in $1997$ from the year $1996$ is:

  $\begin{array}{l}=196.0-190.1\\ =5.9\text{ millions}\end{array}$

The decrease in number of pairs of footwear in $1998$ from the year $1997$ is:

  $\begin{array}{l}=190.1-163.2\\ =26.9\text{ millions}\end{array}$

The decrease in number of pairs of footwear in $1999$ from the year $1998$ is:

  $\begin{array}{l}=163.2-120.9\\ =\text{42}\text{.3 millions}\end{array}$

The decrease in number of pairs of footwear in $2000$ from the year $1999$ is:

  $\begin{array}{l}=120.9-96.5\\ =\text{24}\text{.4 millions}\end{array}$

The decrease in number of pairs of footwear in $1999$ from the previous year is $42.3\text{ millions}$ which is the most as compared to others.

Therefore,

Percent of change in number of pairs of footwear is:

  $\begin{array}{l}p\%=\frac{42.3}{163.2}\left[\text{Substitute}\right]\\ p\%\simeq 0.2591=25.9\%\left[\text{Divide}\text{. Then write decimal as a percent}\right]\end{array}$

Conclusion:

Hence,

The decrease in number of pairs of footwear in the year $1999$ from the previous year is $42.3\text{ millions}$ which is maximum as compared to others and the percent of change is about $25.9\%$ .

iii.

To determine

To conclude and explain from the graph that the footwear manufactures are making less money.

Answer to Problem 25E

No, it cannot be concluded from the graph that manufacturers are making less money from $1996$ to $2000$ since the graph does not indicate the amount that is made per pair of shoes. Also, it is possible that the decrease might be because the manufacturers are having the shoes made for them outside of the United States.

Explanation of Solution

Given information:

Consider, the information provided in the expression,

  

The pairs of footwear manufactured in the year $1996$ is $196.0\text{ millions}$ .

The pairs of footwear manufactured in the year $1997$ is $190.1\text{ millions}$ .

The pairs of footwear manufactured in the year $1998$ is $163.2\text{ millions}$ .

The pairs of footwear manufactured in the year $1999$ is $120.9\text{ millions}$ .

The pairs of footwear manufactured in the year $2000$ is $96.5\text{ millions}$ .

Conclusion and Explanation:

No, it cannot be concluded from the graph that manufacturers are making less money from $1996$ to $2000$ since the graph does not indicate the amount that is made per pair of shoes. Also, it is possible that the decrease might be because the manufacturers are having the shoes made for them outside of the United States.