Runaround Corporation sells running shoes and during January they ran production machines for 20,000 hours total and incurred $9,000 in maintenance costs. During July they ran production machines for 14,000 hours total and incurred $7,200 in maintenance costs. Based on this data, what will total maintenance costs be if the machines are run for 16,500 hours?
A)$7,950
B)$112,545
C)$11,925
D)Cannot determine from the information given.

Question

Quizplus · Accepted Answer

We can use the information given in the problem to find a linear relationship between maintenance costs and hours run. Let C be the total maintenance cost, and H be the total hours run. We can write two equations based on the information given:
9000 = a(20000) + b
7200 = a(14000) + b
where a and b are constants (the slope and intercept of the linear relationship).

Solving for a and b, we get:
a = (9000 - 7200)/(20000 - 14000) = 0.3
b = 7200 - 0.3(14000) = 2800

So the linear equation is:
C = 0.3H + 2800

To find the maintenance cost for 16,500 hours, we can simply plug in H = 16,500:
C = 0.3(16500) + 2800 = 7,950

Therefore, the total maintenance cost if the machines are run for 16,500 hours will be $7,950. The answer is (A).

Runaround Corporation Sells Running Shoes and During January They Ran