Chapter 6.4, Problem 10PPS

To determine

To find: an equation relating the sale price to the regular price and the cost on a pair of $29 jeans on sale.

Answer to Problem 10PPS

The cost of a pair of $29 jeans is $7.25.

Explanation of Solution

Given information:

A store is having a sale where all jeans are $\frac{1}{4}$ off the regular price.

Concept used:

Two quantities are proportional if they have a constant ratio or rate.

Proportional relationships can also be described using equations of the form $y=kx$ , where $k$ is constant ratio. The constant ratio called the constant of proportionality.

Calculation:

A store is giving $\frac{1}{4}$ off on all jeans of sales of regular price.

Assume that $S$ is the selling price of the jeans and $r$ is the regular price of the jeans in a store.

Find the constant of proportionality.

  $\begin{array}{l}\frac{\text{selling}\text{price}}{\text{regular}\text{price}}=\frac{1}{4}\\ \frac{\text{selling}\text{price}}{\text{regular}\text{price}}=0.25\end{array}$

That is, the selling price of the jeans is about 0.25 times the regular price.

Therefore, the corresponding mathematical equation is,

  $S=0.25r$

The following diagram describes this situation:

The cost of a pair of $29 jeans is,

  $\begin{array}{c}S=0.25r\text{Write}\text{the}\text{equation}\text{.}\\ =0.25\times 29\text{Replace}\text{r}\text{with}\text{29}\\ \text{=7}\text{.25}\text{Multiply}\end{array}$

Hence, the cost of a pair of $29 jeans is $7.25.