A base logistics center is processing a shipment of 2,400 supply crates. Over three days, … — Armed Services Vocational Aptitude Battery (ASVAB)

A base logistics center is processing a shipment of 2,400 supply crates. Over three days, the following portions of the total shipment were processed:

- Monday: $31.25\%$ of the total shipment
- Tuesday: $\frac{5}{12}$ of the total shipment
- Wednesday: $0.125$ of the total shipment

How many supply crates remain to be processed?

Answer: 350 crates

Answer

350

The total amount processed is found by converting all values to fractions:

31.25\%

becomes

\frac{5}{16}

and

0.125

becomes

\frac{1}{8}

. Adding these to

\frac{5}{12}

using a common denominator of 48 gives

\frac{41}{48}

processed. The remaining

\frac{7}{48}

of the 2,400 total crates equals 350 crates.

Step-by-Step Solution

Convert

31.25\%

and

0.125

to fractions.

31.25\% = \frac{5}{16}

and

0.125 = \frac{1}{8}

Working in a single format (fractions) is the most precise way to add parts of a whole without losing exact values.

Find the least common denominator (LCD) for

\frac{5}{16}

\frac{5}{12}

, and

\frac{1}{8}

The LCD for 16, 12, and 8 is 48.

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

Convert each fraction to have a denominator of 48 and sum them together.

\frac{15}{48} + \frac{20}{48} + \frac{6}{48} = \frac{41}{48}

This calculates the total fraction of the shipment that has already been processed over the three days.

Subtract the processed fraction from 1 to find the remaining fraction.

1 - \frac{41}{48} = \frac{7}{48}

The question asks for the remaining amount of crates, not the completed amount.

Multiply the remaining fraction by the total number of crates (2,400).

\frac{7}{48} \times 2400 = 7 \times 50 = 350

This converts the fractional remainder back into the actual physical quantity of crates.

Key Concept

Converting percentages and decimals to fractions to efficiently sum portions of a whole, and applying a fractional remainder to a total quantity.

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