Question

Two cars get an oil change at the same service center. Each customer is charged a fee x (in dollars) for the oil change, plus y dollars per quart of oil used. The oil change for the car that requires 5 quart of oil costs $22.45. The oil change for the car that requires 7 quarts of oil costs $25.45.

Find the fee and costs per quart of oil

Answer 1

Basic fee = $14.95

1.5 dollars per quart of oil

Explanation:

Each customer is charged a fee x (in dollars) for the oil change, plus y dollars per quart of oil used.

The oil change for the car that requires 5 quart of oil costs $22.45.

`x+5y=22.45`

`x=22.45-5y`

The oil change for the car that requires 7 quarts of oil costs $25.45.

`x+7y=25.45`

`x=25.45-7y`

Both equation having x

so make it equal and solve for y

`22.45-5y=25.45-7y`

Add 7y on both sides

`22.45+2y=25.45`

subtract 22.45 from both sides

`2y=3\\y=1.5`

now plug in 1.5 for y and solve for x

`x=22.45-5y\\x=22.45-5(1.5)\\x=14.95\\`