Question

Elena wants to earn at least $180 a week to help her parents with bills. She determines that she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can only work 13 hours per week. Write and graph a system of linear inequalities that shows the number of hours she can work so she can help her parents. Use x for the number of hours babysitting and y for the number of hours bagging groceries.

Answer 1

$\begin{gathered} 15x+10y=180 \\ \\ x+y=13 \end{gathered}$

So, the system will be the presented, then:

$\begin{gathered} 15x+10y=180 \\ \\ x=-y+13 \end{gathered}$

Now, we will have that:

$\begin{gathered} 15(-y+13)+10y=180\Rightarrow-15y+195+10y=180 \\ \\ \Rightarrow-5y=-15\Rightarrow y=3 \end{gathered}$

Then:

$x+3=13\Rightarrow x=10$

So, the total hours babysitting should be 10 and bagging groceries should be 3.