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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.

Respuesta :

[tex]\begin{gathered} 15x+10y=180 \\ \\ x+y=13 \end{gathered}[/tex]

So, the system will be the presented, then:

[tex]\begin{gathered} 15x+10y=180 \\ \\ x=-y+13 \end{gathered}[/tex]

Now, we will have that:

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

Then:

[tex]x+3=13\Rightarrow x=10[/tex]

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