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 $20.30. The oil change for the other car required 7 quarts of oil and cost $22.80. How much is the labor fee and how much is each quart of oil?

Answer 1

Labor fee: 14.05 Cost of oil per quart: 1.25

Explanation:

1. Assume that the labor fee is y and cost of oil per quart is x.
2. We can deduce that 5x+y=20.30 because the labor fee doesn't change and there are 5 quarts of oil
3. We can also deduce that 7x+y=22.80 of the same reason
4. Therefore, by eliminating the y at both side, 2x=2.5, therefore, x=1.25
5. Substitute x=1.25 so 6.25+y=20.30, so y=14.05
6. Check: Substitute it to 5x+y, which also makes it to 22.80

Answer 2

1.25$/per quart of oil. 14.05 starting fee.

Explanation:

Give a variable that one quart of oil is o.

5o + starting fee +2.5 = 7o + starting fee

2o = 2.5

o = 1.25

substitute and we know starting fee is 14.05