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 $25.50. The oil change for the other car required 7 quarts of oil and cost $30.00. How much is the labor fee and how much is each quart of oil?

Answer 1

The labor fee is $14.25, each quart of oil costs $2.25.

Explanation:

Let $x be thee price of each quart of oil and $y be a flat fee for labor.

1. If the oil change for one car required 5 quarts of oil, then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50. Thus,

5x+y=25.50.

2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $30.00. Thus,

7x+y=30.00.

3. Subtract from the second equation the first one, then

`7x+y-(5x+y)=30.00-25.50,\\ \\7x+y-5x-y=4.50,\\ \\2x=4.50,\\ \\x=\$2.25.`

Substitute it into the first equation:

`5\cdot 2.25+y=25.50,\\ \\y=25.50-11.25,\\ \\y=\$14.25.`

The labor fee is $14.25, each quart of oil costs $2.25.