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Difficulty: MediumDividing in a Ratio

A communications platoon is distributing a shipment of 8,4008,400 replacement radio batteries among three forward operating bases (FOB Alpha, FOB Bravo, and FOB Charlie) in a ratio of 4:5:64:5:6, respectively. Based on this ratio, how many batteries will FOB Charlie receive?

Answer: 3360 batteries

Answer

FOB Charlie will receive 3,360 batteries.
The total ratio parts sum to 15 (4 + 5 + 6). Dividing the total 8,400 batteries by 15 yields 560 batteries per part. FOB Charlie corresponds to the '6' in the ratio, so multiplying 560 by 6 gives the correct allocation of 3,360 batteries.

Step-by-Step Solution

1
Calculate the total number of ratio parts.
4+5+6=154 + 5 + 6 = 15 parts
To divide a total quantity in a specific ratio, you first need to determine the total number of equal parts that make up the whole.
2
Determine the amount of batteries in a single part.
8,400÷15=5608,400 \div 15 = 560 batteries per part
Dividing the total number of batteries by the total number of parts establishes the baseline value of one unit in the ratio.
3
Calculate FOB Charlie's share.
560×6=3,360560 \times 6 = 3,360 batteries
Since FOB Charlie receives 6 parts of the ratio, multiplying the value of a single part by 6 gives their final allocation.

Key Concept

To divide a quantity into a given ratio, find the total number of parts by summing the ratio values, divide the total quantity by this sum to find the value of one part, and then multiply by the desired part's ratio value.
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Topics

Dividing in a Ratio

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