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?
21p + 15r <= 185
p + r >= 5
Let p represent the number of gallons of paint and r represent the number of gallons of primer.
The cost of paint is $21 per gallon, so the cost of p gallons of paint is 21p dollars.
The cost of primer is $15 per gallon, so the cost of r gallons of primer is 15r dollars.
The total cost of paint and primer should not exceed $185, so we can write the inequality:
21p + 15r <= 185
Brett needs at least 5 gallons of paint and primer in total, so we can write the inequality:
p + r >= 5
Therefore, the system of inequalities representing Brett's situation is:
21p + 15r <= 185
p + r >= 5
To represent Brett's situation with a system of inequalities, we need to set up the constraints based on the given information.
Let's start by considering the cost constraint. The total cost of the paint and primer should not exceed $185. We can express this constraint using the cost per gallon and the number of gallons of paint and primer as follows:
21p + 15r <= 185
Next, let's consider the quantity constraint. Brett needs at least 5 gallons of paint and primer in total. We can express this constraint using the number of gallons of paint and primer as follows:
p + r >= 5
Therefore, the system of inequalities that represents Brett's situation is:
21p + 15r <= 185
p + r >= 5