Question

A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5 cm longer than the second?

Answer 1

Given:

Total length of the board = 91 cm

Let the length of the shortest piece = x cm

Then,
Second piece = (x + 3) cm
Third piece = 2x cm

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Condition 1: Total length constraint

x + (x + 3) + 2x ≤ 91

4x + 3 ≤ 91

4x ≤ 88

x ≤ 22

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Condition 2: Third piece is at least 5 cm longer than the second

Third piece ≥ Second piece + 5

2x ≥ (x + 3) + 5

2x ≥ x + 8

x ≥ 8

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Possible values of x:

From both conditions,

8 ≤ x ≤ 22

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Graphical Representation on Number Line:

Closed circles at 8 and 22,
with the region between 8 and 22 shaded.

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Final Answer:

The possible lengths of the shortest board are
between 8 cm and 22 cm (inclusive).