Problem Solving

During the four years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the remainder. The cost of insurance was 3 times the cost of financing, and together these two costs accounted for 1/5 of the total. If the only other expenses were taxes and license fees, then the cost of financing was how much more or less than the cost of taxes and license fees?

(A) $1,500 more
(B) $1,200 more
(C) $100 less
(D) $300 less
(E) $1,500 less

We are given that Mrs. Lopez's total car expenses during the four years were $18,000.

Since fuel and maintenance (F&M) costs accounted for 1/3 of the total expenses:

F&M costs = 1/3(18,000) = $6,000.

Since depreciation accounted for 3/5 of the remainder:

depreciation = 3/5(18,000 - 6,000) = 3/5 (12,000) = $7,200.

Since we don't know the actual cost of insurance or financing except that the cost of insurance was 3 times the cost of financing, and the two costs together accounted for 1/5 of the total expenses, we can let x = cost of financing and 3x = cost of insurance, and create the following equation:

x + 3x = 1/5(18,000)

4x = 3,600

x = 900

So the cost of financing was $900 and the cost of insurance was 3($900) = $2,700.

The last expense is taxes and license (T&L) fees, so T&L fees must be the difference between the total expenses and the sum of all the items (F&M, depreciation, insurance, and financing) mentioned above. Thus:

T&L fees = 18,000 - (6,000 + 7,200 + 900 + 2,700) = 18,000 - 16,800 = $1,200

Finally, we are asked: "the cost of financing was how much more or less than the cost of taxes and license fees?" Since the cost of financing was $900 and T&L fees were $1,200, the cost of financing is $300 less than that of T&L fees.

Answer: D