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

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"