What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second?

Question

A man wants to cut three lengths from a single piece of board of length 91cm. The second length is to be 3cm 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 5cm longer than the second?

Answer 1

Solution:
Let x be the shortest board.

Then x + 3 is the second piece and 2x is the third piece.

x + (x + 3) + 2x ≤ 91
and 2x ≥ (x + 3) + 5

x + (x + 3) + 2x≤ 91
4x + 3 ≤ 91
4x ≤ 91 – 3
4x ≤88
x ≤ 44/2

2x ≥ (x + 3) + 5
2x ≥ x + 8
x ≥ 8

i.e, 8 ≤ x < 22

Thus the possible lengths of the shortest board is at least 8cm long but not more than 22cm long.