2 Sarah works for a maximum of 40 hours per week. She needs to make at least $400 in order to cover her expenses. Her office job pays
$12 per hour and her babysitting job pays $10 per hour.
Which system of inequalities can be used to determine the number of hours she should spend working in office (x) and the number of
hours she should spend babysitting (/) to cover her expenses?

x + y ≤ 40

10x + 12 y ≥ 400

x ≥ 0

y ≥ 0

Step-by-step explanation:

System of Inequalities

In order to model the situation stated in the problem, we'll call the following variables:

x = number of hours Sarah spends in the office

y = number of hours Sarah spends babysitting

She works for a maximum of 40 hours per week. This condition leads us to the inequality:

x + y ≤ 40

Her office job pays $12 per hour and her babysitting job pays $10 per hour.

She needs to make at least $400 per week in order to cover her expenses, thus:

10x + 12 y ≥ 400

Two obvious conditions could be added to the set of inequalities:

x ≥ 0

y ≥ 0

The system of inequalities is:

x + y ≤ 40

10x + 12 y ≥ 400

x ≥ 0

y ≥ 0