Question

Please help with this problem.

MODELING REAL LIFE A service center charges a fee of X dollars for an oil change plus y dollars per quart of oil used. Customer A receives 5 quarts of oil and pays a total of $37.45. Customer B receives 7 quarts of oil and pays a total of $46.45. Find the fee and cost per quart of oil.
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FREE $ -
COST PER QUART OF OIL $ -

Answer 1

The fee is $14.95

The cost per qt of oil is $4.50

Explanation:

Let f = fee, and let q = cost of 1 qt of oil.

Customer A:

5q + f = 37.45

Customer B:

7q + f = 46.45

Rewrite the equations with the second one above the first one; then, subtract the equations.

7q + f = 46.45

(-) 5q + f = 37.45

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2q = 9

Divide both sides by 2.

q = 4.5

Use the first equation:

5q + f = 37.45

Substitute 4.5 for q and solve for f.

5(4.5) + f = 37.45

22.5 + f = 37.45

Subtract 22.5 from both sides.

f = 14.95

Answer:

The fee is $14.95

The cost per qt of oil is $4.50