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Question

Difficulty: MediumDividing in a Ratio

A naval supply officer is allocating a $4,500\$4,500 monthly discretionary budget among three ship departments—Deck, Engineering, and Operations—in a ratio of 4:5:64:5:6, respectively. Calculate the specific funding amounts based on this ratio.

Answer:The Engineering department will receive $【1500】\$【1500】, and the Operations department will receive $【600】\$【600】 more than the Deck department.

Answer

The Engineering department receives $1,500\$1,500, and the Operations department receives $600\$600 more than the Deck department.
The total budget of $4,500\$4,500 is divided into 1515 equal parts (4+5+64 + 5 + 6). Each part is worth $300\$300 ($4,500÷15\$4,500 \div 15). The Engineering department receives 55 parts, which amounts to $1,500\$1,500 (5×$3005 \times \$300). The Operations department receives 66 parts and the Deck department receives 44 parts. The difference between them is 22 parts (6−46 - 4), which amounts to $600\$600 (2×$3002 \times \$300).

Step-by-Step Solution

1
Calculate the total number of parts in the ratio.
4+5+6=154 + 5 + 6 = 15 total parts.
The total budget must be divided by the sum of the ratio numbers to find the value of a single part.
2
Determine the monetary value of one part.
$4,500÷15=$300\$4,500 \div 15 = \$300.
This establishes the base unit value that can be multiplied by each department's respective ratio number.
3
Calculate the amount allocated to the Engineering department (second value in the ratio).
5×$300=$1,5005 \times \$300 = \$1,500.
This provides the answer for the first blank.
4
Calculate the difference between the Operations department (6 parts) and the Deck department (4 parts).
Difference in parts: 6−4=26 - 4 = 2 parts. Monetary difference: 2×$300=$6002 \times \$300 = \$600.
This provides the answer for the second blank without needing to calculate the full amounts for both departments.

Key Concept

Dividing a quantity in a given three-part ratio by finding the sum of the parts and the value of a single unit.
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Topics

Dividing in a Ratio

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