Question

Leah would like to earn at least 150 per month. She babysits for $10 per hour and works at an ice cream shop for$12 per hour.Leah cannot work more than a total of 25 hours per month.Let x represent the number of hours leah babysits and let y represent the number of hours leah works at the ice cream shop

Answer 1

The solution in the attached figure

Explanation:

The question is

Write and solve a system of inequalities that models this situation

Let

x ---> represent the number of hours Leah babysits

y ---> represent the number of hours Leah works at the ice cream shop

we know that

Leah would like to earn at least 150 per month

The term "at least" means "greater than or equal to"

so

`10x+12y\geq 150` ----> inequality A

The solution of the inequality A is the shaded area above the solid line
`10x+12y= 150`

The slope of the solid line A is negative m=-5/6

The y-intercept of the solid line A is (0,12.5)

The x-intercept of the solid line A is (15,0)

Leah cannot work more than a total of 25 hours per month

`x+y\leq 25` ----> inequality B

The solution of the inequality B is the shaded area below the solid line B
`x+y=25`

The slope of the solid line B is negative m=-1

The y-intercept of the solid line B is (0,25)

The x-intercept of the solid line B is (25,0)

using a graphing tool

The solution of the system of inequalities is the shaded area above the solid line A and below the solid line B

see the attached figure