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 $23.40. The oil change for the other car required 7 quarts of oil and cost $26.90. How much is the labor fee and how much is each quart of oil

Answer: Oil quart = $1.75 each and Labor fee = $14.65

Explanation:

First Car

5 oil quarts plus flat fee for labor = 23.40

Second Car

7 oil quarts plus flat fee for labor = 26.90

Labor is fixed which means the cost of labor for servicing the first car is equal to the cost of labor for servicing the second car. Hypothetically speaking if we used the same number of oil quarts in both cars, the cost of servicing each car would be the same. The cost would be equal to $23.40, but now 2 more oil quarts were used in servicing the second car and costs rose to $26.90.

We know that labor is fixed therefore the change in total costs from $23.40 to $26.90 is caused by the extra two more oil quarts used in the second car. Therefore this means that the cost of 2 oil quarts is $3.50 (26.90 - 23.40) which tells us that 1 quarter of oil is equal to $1.75 ($3.5 / 2).

Cost servicing First Car

total cost of oil = 5 oil quarts x 1.75 = $8.75

Labor fee = 23.40 - 8.75 = $14.65

Cost of servicing the Second car

total cost of oil = 7 oil quarts x 1.75 = $12.25

Labor fee = 26.90 - 12.25 = $14.65

Oil quart = $1.75 each and Labor fee = $14.65