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Difficulty: EasyDividing in a Ratio

During a base renovation, a carpenter cuts a 55-foot wooden board into two pieces. If the lengths of the two pieces are in a ratio of 2:32:3, what is the length of the shorter piece in inches?

  1. 2424Answer
  2. B
    3636
  3. C
    4040
  4. D
    22

Answer

The shorter piece is 2424 inches long.
First, convert the 55-foot board to inches by multiplying by 1212, which gives 6060 inches. The ratio 2:32:3 means there are 2+3=52 + 3 = 5 total equal parts. Dividing the 6060-inch board by 55 gives 1212 inches per part. The shorter piece is 22 parts, so 2×12=242 \times 12 = 24 inches.

Step-by-Step Solution

1
Convert the total length of the board from feet to inches.
5×12=605 \times 12 = 60 inches.
The question asks for the final answer in inches, so it is easiest to work in inches from the start.
2
Find the total number of parts in the ratio.
2+3=52 + 3 = 5 total parts.
A ratio of 2:32:3 means the whole board is divided into 55 equal segments.
3
Determine the length of one single part.
60÷5=1260 \div 5 = 12 inches per part.
Dividing the total length by the total number of parts gives the value of one part.
4
Calculate the length of the shorter piece.
12×2=2412 \times 2 = 24 inches.
The shorter piece represents 22 parts of the ratio.

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 number to find the value of one part, and multiply by the relevant ratio term. Always ensure units are consistent.
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Topics

Dividing in a Ratio

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