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? [Hint: If x is the length of the shortest board, then x, (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x + (x + 3) + 2x 91 and 2x ≥ (x + 3) + 5].

Question

Philoid · Accepted Answer

Let us assume the length of the shortest piece be x cm

∴ According to the question, length of the second piece = (x + 3) cm

And, length of third piece = 2x cm

As all the three lengths are to be cut from a single piece of board having a length of 91 cm

∴ x + (x + 3) + 2x ≤ 91 cm

= 4x + 3 ≤ 91

= 4x ≤ 88

= x ≤ 22 …(i)

Also, it is given in the question that, the third piece is at least 5 cm longer than the second piece

∴ 2x ≥ (x+3) + 5

2x ≥ x + 8

x ≥ 8 …(ii)

Thus, from equation (i) and (ii) we have:

8 ≤ x ≥ 22

Hence, it is clear that the length of the shortest board is greater than or equal to 8 cm and less than or equal to 22 cm