Question

Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $25.10. The oil change for the other car required 7 quarts of oil and cost $29.60. How much is the labor fee and how much is each quart of oil?

The labor fee is $____, and each quart of oil costs $_____.

Answer 1

The labor fee = $13.85 and

the cost of each quart of oil = $2.25

Explanation:

Let x be the flat fee for labor and y be th cost of each quart of oil.

Then, the verbal models for the cars are:

x + 5y = 25.10 --- (1) and

x + 7y = 29.60 --- (2)

(2) - (1) gives,

2y = 4.50

Divide both sides by 2.

y = 2.25

Substitute in (1), we get,

x + 5(2.25) = 25.10

x + 11.25 = 25.10

x = 25.10 - 11.25

x = 13.85

Hence,

The labor fee = $13.85 and

the cost of each quart of oil = $2.25