Chapter 4.4, Problem 83SR

To determine

Find the number of hours Terrel work at each job for earning at least given money per week.

Answer to Problem 83SR

The number of hours Terrel work at each job for earning at least $\$120$ per week is $15$ hours.

Explanation of Solution

Given:

Terrel makes $\$10$ and $\$12$ an hour for cutting grass and leaves respectively. He can not work more than $15$ hours per week. The given earning is $\$120$ per week.

Calculation:

Let

The number of hours (cutting grass) $=x$

The number of hours (raking leaves) $=y$

From question

  $\begin{array}{l}x+y\le 15\\ 10x+12y\ge 120\end{array}$

Draw a graph for the inequality of the systems using graphing utility.

  

From the graph, the number of hours Terrel work at each job for earning at least $\$120$ per week is $15$ hours.