Question

Keith will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $44 and costs an additional $0.15 per mile driven. When do the two plans cost the same?

Answer 1

325 miles

Explanation:

This is a good question, a real life example.

So what we need to do is come up with an expression for the total cost in each scenario. There's a fixed cost in each, and then a variable cost based on how many miles you drive the car.

For the first one:

57 + 0.11x

That represents what it would cost when you bring the car back with x miles driven. 0.11 $/mile times miles means the miles cancel out and we're left with unit of dollars. Which matches the $57. Always pay attention to units.

For the second one:

44 + 0.15x

Do you follow those? Base cost in each case, plus the variable mileage cost.

"When do the two plans cost the same" tells us that we should set those two expressions equal to each other:

0.11x + 57 = 0.15x + 44

Then to find the unknown mileage x, we just solve for x. I moved the 0.11x term to the right and the 44 to the left:

0.04x = 13

x = 13/0.04 = 325 miles