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

Let the length of the shortest piece be x cm .

Then the length of the second piece and the third piece are (x+3) cm and 2x cm respectively.

Since the three lengths are to be cut from a single piece of board of length 91 cm,

x+(x+3)+2x ≤ 91

⇒4x+3≤91

⇒4x≤91−3

⇒4x≤88

⇒ 44x≤ 488

⇒x≤22-----(i)

Also the third piece is at least 5 cm longer than the second piece.

∴2x≥(x+3)+5

⇒2x≥x+8

⇒x≥8....(2)

From (1) and (2) we obtain

8≤x≤22

Thus the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm.

Hope it will help you