A Boatswain's Mate needs 12 gallons of deck paint for a resurfacing project. In the paint … — Armed Services Vocational Aptitude Battery (ASVAB)

A Boatswain's Mate needs $12$ gallons of deck paint for a resurfacing project. In the paint locker, they find three partially filled buckets containing $4 \frac{2}{3}$ gallons, $2 \frac{1}{4}$ gallons, and $1 \frac{5}{6}$ gallons of the correct paint. If they combine all the paint from these buckets, how many additional gallons of paint do they need to reach the required $12$ gallons?

$3 \frac{1}{4}$ Answer
B
$4 \frac{3}{4}$
C
$4 \frac{5}{13}$
D
$8 \frac{3}{4}$

Answer

The Boatswain's Mate needs an additional

3 \frac{1}{4}

gallons of paint.

The correct result is found by first combining the available quantities of paint. Since the fractions have unlike denominators (

3

4

, and

6

), a common denominator of

12

is used:

4 \frac{8}{12} + 2 \frac{3}{12} + 1 \frac{10}{12} = 7 \frac{21}{12}

, which simplifies to

8 \frac{3}{4}

gallons. To determine the remaining amount needed, subtract this total from the required

12

gallons. By regrouping

12

11 \frac{4}{4}

, the final step becomes

11 \frac{4}{4} - 8 \frac{3}{4}

, yielding

3 \frac{1}{4}

gallons.

Step-by-Step Solution

Find a common denominator to add the fractions of paint currently available.

The least common denominator for

3

4

, and

6

12

. Convert the fractions:

4 \frac{2}{3} = 4 \frac{8}{12}

2 \frac{1}{4} = 2 \frac{3}{12}

, and

1 \frac{5}{6} = 1 \frac{10}{12}

Fractions must have the same denominator before they can be added together accurately.

Add the converted mixed numbers to find the total amount of paint on hand.

Add the whole numbers:

4 + 2 + 1 = 7

. Add the fractions:

\frac{8}{12} + \frac{3}{12} + \frac{10}{12} = \frac{21}{12}

. Combine them to get

7 \frac{21}{12}

. Simplify the improper fraction

\frac{21}{12}

1 \frac{9}{12}

, which adds to the whole number to become

8 \frac{9}{12}

. Reduced to simplest form, this is

8 \frac{3}{4}

gallons.

This establishes the total combined volume of paint from the three buckets.

Subtract the total paint on hand from the total paint required to find the difference.

Subtract

8 \frac{3}{4}

from

12

. To do this, borrow

1

from the whole number

12

to create a mixed number with a matching denominator:

11 \frac{4}{4} - 8 \frac{3}{4} = 3 \frac{1}{4}

gallons.

Subtracting the available amount from the required total determines exactly how much more paint is needed.

Key Concept

Adding mixed numbers with unlike denominators and correctly borrowing to subtract a mixed number from a whole number.

Question

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