Bunuel wrote:
There are 4 quarts in a gallon. A gallon of motor oil sells for $12 and a quart of the same oil sells for $5. The owner of a rental agency has 6 machines and each machine needs 5 quarts of oil. What is the minimum amount of money she must spend to purchase enough oil?
(A) $84
(B) $94
(C) $96
(D) $102
(E) $150
Approach I - RemainderI treated this as a remainder question.
She needs 30 quarts of oil:
6 machines * 5 quarts ea = 30 quarts
1 gallon = 4 quarts
Divide 30 by 4.
Because there are 4 quarts in one gallon, the division will yield the number of gallons plus leftover quarts --
That is, the remainder will be quarts that don't "fit" and have to be bought separately.
\(\frac{30}{4}\) = 7 + R2 (quarts)
(7 gallons * $12 per gallon) = $84
(2 quarts * $5 per quart) = $10
$84 +10 = $94 is the minimum
Answer B
Approach II - Conversion, units will cancelM = machines
Q = quarts
G = gallons
\((6M *\frac{5Q}{1M}*\frac{1G}{4Q})= \frac{30G}{4}= 7\frac{2}{4}G\)
7 gallons plus
\(\frac{2}{4}\) of a gallon
1 gallon=\(\frac{4}{4}\) quarts
You need 2 of those 4 quarts.
Then multiply 7 gallons and 2 quarts by cost per each, and sum, as above.
Minimum is $94
Answer B
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