Question

Brett wants to paint his master bedroom. The paint costs $21 per gallon and the primer costs $15 per gallon. He does not want to exceed $185 for the paint and primer. He has determined that he needs at least 5 gallons of paint and primer in total. If p represents the number of gallons of paint and r represents the number of gallons of primer, which system of inequalities represents Brett’s situation?

Answer 1

`21p + 15r \leq 185`

`p + r \geq 5`

Step-by-step explanation:

Two inequalities can be derived from the question.

1. Total Cost Inequality

If paint (p) costs $21 per gallon, primer (r) costs $15 per gallon, and Brett does not want to exceed $185, we can represent this by the inequality below.

`21p + 15r \leq 185`.

This means total cost of paint and primer will be less than or equal to $185.

2. Total Quantity Inequality

Brett determined that he needs at least 5 gallons in total, and we represent this by the inequality below.

`p + r \geq 5`

This means total quantity of paint and primer must be greater than 5.