Chapter 7.2, Problem 80E

To determine

To find : the number of shoes of different styles sold.

Answer to Problem 80E

The number of one style and other style shoes are $170$ and $80$ respectively.

Explanation of Solution

Given information :

Rate of one style shoes $=\$79.50\text{ per pair}$

Rate of other style shoes $=\$89.95\text{ per pair}$

Total number of shoes sold $=250$

Total amount collected by selling shoes $=\$20713.40$

Calculation :

Let the number of one style shoes and other style are denoted by $x$ and $y$ respectively.

According to the question

  $x+y=250$  ...(1)

  $\left(79.50\right)x+\left(89.95\right)y=20713.40$  ...(2)

Multiply equation (1) by $79.50$ :

  $79.50x+79.50y=19875$  ...(3)

Solve equation (2) and (3) by elimination method:

  $\underset{\_}{\begin{array}{l}\text{ 79}\text{.50}x+89.95y=20713.40\\ \text{- 79}\text{.50}x+79.50y=19875\end{array}}$

  $\begin{array}{l}\text{ 10}\text{.45y}=838.4\\ \text{ y}=\frac{838.4}{10.45}\\ \text{ y}=80.22\\ \text{ y}\approx \text{80}\end{array}$

Calculate value of $x$ by putting value of $y$ in equation (1):

  $\begin{array}{l}x+y=250\\ x=250-80\\ x=170\end{array}$

Therefore,the number of one style and other style shoes are $170$ and $80$ respectively