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Difficulty: EasyDividing in a Ratio

A communications specialist is preparing a field antenna and needs to cut a 6060-foot spool of copper wire into two sections in a ratio of 7:37:3.

Answer:The longer section of the wire will be 【42】 feet long.

Answer

The longer section of the wire will be 42 feet long.
The wire is divided into 7+3=107 + 3 = 10 total parts. Since the total length is 6060 feet, each part is equal to 60÷10=660 \div 10 = 6 feet. The longer section is 77 parts, so its length is 7×6=427 \times 6 = 42 feet.

Step-by-Step Solution

1
Find the total number of parts in the ratio.
7+3=107 + 3 = 10 total parts.
The total length of the wire is divided into this many equal parts.
2
Calculate the length of one single part.
60÷10=660 \div 10 = 6 feet per part.
Dividing the total length by the total number of parts gives the value of one part.
3
Determine the length of the longer section.
7×6=427 \times 6 = 42 feet.
The longer section corresponds to the larger number in the ratio, which is 7 parts.

Key Concept

To divide a quantity in a given ratio, find the total number of parts by adding the ratio terms, divide the total quantity by this sum to find the value of one part, and then multiply by the specific ratio term.
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Topics

Dividing in a Ratio

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