Final answer:
The fee for the service center is $15.00 and the cost per quart of oil is $4.50. This was determined by creating two equations based on the amounts paid by two customers and the number of quarts of oil they received, and then solving the system of equations.
Step-by-step explanation:
To find the fee for the service center and the cost per quart of oil, we can set up two equations using the information given for Customer A and Customer B.
For Customer A who receives 5 quarts of oil and pays $37.45, we can write the equation:
A: x + 5y = 37.45
For Customer B who receives 7 quarts of oil and pays $46.45, we can write the equation:
B: x + 7y = 46.45
We now have a system of linear equations. To solve it, we can use the method of substitution or elimination. If we subtract equation A from B, we get:
2y = 46.45 - 37.45
2y = 9
y = 9 / 2
y = 4.50
Now that we know y, which is the cost per quart of oil, we can substitute it back into equation A and solve for x.
x + 5(4.50) = 37.45
x = 37.45 - 22.50
x = 15.00
Therefore, the fee for the service center is $15.00, and the cost per quart of oil is $4.50.