A logistics officer is allocating a stockpile of 112 \frac{1}{2} gallons of specialty avia… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics officer is allocating a stockpile of $112 \frac{1}{2}$ gallons of specialty aviation lubricant. The primary maintenance hangar is allocated $\frac{3}{5}$ of the total stockpile. The remaining lubricant is to be divided equally among $4$ flightline repair vehicles. How many gallons of lubricant will each repair vehicle receive?

$11 \frac{1}{4}$ Answer
B
$16 \frac{7}{8}$
C
$180$
D
$7 \frac{13}{14}$

Answer

The correct answer is

11 \frac{1}{4}

gallons, which is calculated by finding the remaining portion of the stockpile and dividing it equally among the four vehicles.

The correct answer accurately determines that

\frac{2}{5}

of the total stockpile remains, calculates that remaining amount to be

45

gallons, and then correctly divides those

45

gallons equally among the

4

repair vehicles to yield

11 \frac{1}{4}

gallons.

Step-by-Step Solution

Determine the fraction of the stockpile that remains for the repair vehicles.

1 - \frac{3}{5} = \frac{2}{5}

The primary hangar is allocated

\frac{3}{5}

of the total, meaning the rest is left for the vehicles.

Calculate the volume of the remaining lubricant.

\frac{2}{5} \times 112 \frac{1}{2} = \frac{2}{5} \times \frac{225}{2} = \frac{450}{10} = 45

gallons.

Multiplying the remaining fraction by the total initial volume gives the exact gallons available.

Divide the remaining volume equally among the 4 repair vehicles.

45 \div 4 = \frac{45}{4} = 11 \frac{1}{4}

gallons.

The total remaining amount must be distributed evenly to determine each vehicle's individual share.

Key Concept

Fraction Multiplication and Division in Context

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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