Question

lan is working two summer jobs, making $19 per hour lifeguarding and making $9per hour clearing tables. In a given week, he can work no more than 14 total hoursand must earn a minimum of $180. If x represents the number of hours lifeguardingand y represents the number of hours clearing tables, write and solve a system ofinequalities graphically and determine one possible solution.Inequality 1: y 24plot switch shadeInequality 2: y 24plotswitch shade2019181716151413121110Yes

Answer 1

Given:

Lan is working two jobs:

1) $19 per hour life guarding

2) $9 per hour clearing tables

The total hours per week = 14

He must earn a minimum of $180

Let x represents the number of hours life guarding and y represents the number of hours clearing tables

So, we have the following inequalities

`\begin{gathered} x+y\le14 \\ 19x+9y\ge180 \end{gathered}`

We need to solve the inequalities by graph

So, we will graph the lines: x + y = 14 and 19x + 9y = 180

The shaded area represents the solution of the system of inequalities

The following figure represents the solution of the system of inequalities