PSAT Math Grid-Ins Question 146: Answer and Explanation

Question: 146

A high school is going to have its prom and is evaluating two different D.J.s—D.J. A and D.J. B. The first one, D.J. A, has a $300 rental fee and charges $150 per hour. The second one, D.J. B, has a $200 rental fee and charges $175 per hour. After how many hours of performing will the cost for both D.J.s be the same?

Correct Answer: 4

Explanation:

4 Set up equations expressing the total costs for each D.J., where T represents time:

D.J. A's cost: 300 + 150T
D.J. B's cost: 200 + 175T

Set the equations equal to one another, and solve for time:

300 + 150T = 200 + 175T → 100 = 25T → T = 4