Chapter 6.1, Problem 31PPE

To determine

To find: numbers of hours of work would your net earnings from either job be the same.

Answer to Problem 31PPE

13 hours

Explanation of Solution

Given information: there are two jobs first is that who pays you $9 per hour and second pays you $12 per hour but you have to buy a uniform of $39.

Let $x$ be the number of hours that you job.

And let $y$ be your total earning.

The first job pays you $9 per hour and no uniform you have to buy.

Then your total earning in working $x$ hours is $9x$ , and the corresponding equation is $y=9x$ .

Now, the second job pays you $12 per hour and a uniform you have to buy that cost $39.

Then your total earning in working $x$ hours is $12x-39$ , and the corresponding equation is $y=12x-39$ .

The two equations are as follows-

  $\begin{array}{l}y=9x\\ y=12x-39\end{array}$

Solving above equations

  $\begin{array}{l}9x=12x-39\\ \Rightarrow 12x-9x=39\\ \Rightarrow 3x=39\\ \Rightarrow x=\frac{39}{3}=13\end{array}$

Hence, after 13 hours of work net earnings from either job will be same.

And their graphs are given by-