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During the four years that Mrs. Lopez owned her car, she

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by BTGmoderatorDC » Sun Nov 11, 2018 9:40 pm

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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

OA D

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by swerve » Mon Nov 12, 2018 9:50 am
Fuel & Maintenance = 1/3
depreciation = 3/5 of the rest = 3/5*2/3 = 2/5
Insurance = 3 * Financing
Insurance + Finance = 1/5

Let Taxes & License = x

so compute for x

1/3 + 2/5 + 1/5 + x = 1
x= 1/15

Amount of x = 1/15*18000 = 1200 -- (1)

Now I + F = 1/5*18000
but I = 3F
so 4F = 1/5*18000
F= 900 -- (2)

Ans is (2) - (1)...i.e. 300 less
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by [email protected] » Mon Nov 12, 2018 11:09 am
Hi All,

While this question IS wordy, the math behind it is just arithmetic. If you break the prompt into 'pieces', then the work shouldn't be too difficult. The first two sentences tell us that the total car expenses were $18,000, fuel and maintenance costs accounted for 1/3 of THAT total and depreciation accounted for 3/5 of the REMAINDER.

TOTAL = $18,000
Fuel/Maint. = (1/3)($18,000) = $6,000
Remainder = $18,000 - $6,000 = $12,000

Depreciation = (3/5)($12,000) = $7,200

Next, we're told that
Insurance = 3(Financing)
Insurance + Financing = (1/5)($18,000)

Here, we have a 'system' of equations (2 variables and 2 unique equations), so we can solve for both variables...

Insurance + Financing = $3,600
3(Financing) + Financing = $3,600
4(Financing) = $3,600
Financing = $900

Insurance + $900 = $3,600
Insurance = $2,700

At this point, we have....
Total = $18,000
Fuel/Maint. = (1/3)($18,000) = $6,000
Depreciation = (3/5)($12,000) = $7,200
Financing = $900
Insurance = $2,700

$6,000 + $7,200 + $900 + $2,700 = $16,800

This leaves $1,200 for the remaining costs, which we're told are the Taxes and Licensing Fees

Taxes&Licensing = $1,200

The question asks how much more/less the Financing cost was compared to the Taxes&Licensing....

$900 - $1,200 = - $300 = $300 LESS

Final Answer: D

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Rich
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