Chapter 8.8, Problem 6E

To determine

To write and solve:

Alinear system to find the number of each type of shoe to display.

Answer to Problem 6E

There will be 40 styles of court shoes to display.

There will be 80 styles of running shoes to display.

Explanation of Solution

Given:

One wall of a shoe store is used to display court shoes and running shoes. There is enough room on the wall for 120 styles of shoes. Based on past sales, the store manager wants to display twice as many running shoes as court shoes.

Calculation:

Let x represent styles of court shoes.

We have been given that the store manager wants to display twice as many running shoes as court shoes, so styles of running shoes would be $2x$ .

The total styles of shoes are 120. We can represent this information in an equation as:

  $x+2x=120$

Let us solve for x.

  $\begin{array}{l}x+2x=120\\ 3x=120\left(\text{Combining like terms}\right)\\ \frac{3x}{3}=\frac{120}{3}\left(\text{Dividing both sides by 3}\right)\\ x=40\end{array}$

Therefore, there will be 40 styles of court shoes to display.

The styles of running shoes would be $2x\Rightarrow 2(40)=80$ .

Therefore, there will be 80 styles of running shoes to display.