Answer:
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
