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

Let x be the length of the shortest board then x + 3 and 2x are the lengths of the second and third piece, respectively. 

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

4x ≤ 88 and x ≥ 8 

⇒ x ≤ 22 and x ≥ 8 

⇒ 8 ≤ x  ≤ 22. 

∴ The possible length of board is at least 8 cm long but not more than 22 cm long.