We are given the following information
Leah babysits for $5 per hour and works at an ice cream shop for $8 per hour.
She wants to earn at least $120 a month.
Let x denotes the number of hours she babysits and y denotes the number of hours she works at the ice cream shop.
Then we can set up the following inequality
[tex]5x+8y\ge120[/tex]
(at least means equal or greater than)
If Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120?
We have to substitute x = 7 into the above inequality
[tex]\begin{gathered} 5x+8y\ge120 \\ 5(7)+8y\ge120 \\ 35+8y\ge120 \\ 8y\ge120-35 \\ 8y\ge85 \\ y\ge\frac{85}{8} \\ y\ge10.625 \\ y\ge11 \end{gathered}[/tex]
This means she needs to work at least 11 hours at the ice cream shop to earn at least $120.
