Question

If Leah babysits for 7 hours this month, what is the minimum number of hours shewould have to work at the ice cream shop to earn at least $120?Give your answer to the nearest whole hour.

Answer 1

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

`5x+8y\ge120`

(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

`\begin{gathered} 5x+8y\ge120 \\ 5(7)+8y\ge120 \\ 35+8y\ge120 \\ 8y\ge120-35 \\ 8y\ge85 \\ y\ge(85)/(8) \\ y\ge10.625 \\ y\ge11 \end{gathered}`

This means she needs to work at least 11 hours at the ice cream shop to earn at least $120.