Question

26.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 tobe twice as long as the shortest. What are the possible lengths of the shortestboard if the third piece is to be at least 5cm longer than the second?rtest board, then xlengths of the second and third piece, respectively. Thus, x+(x +3)+2xs 91 and2x 2 (x 3) 5],

Answer 1

Let

x be the length of the shortest board. Then, length of the second board is x+3. And length of the third board is 2x.

Since, the maximum sum of length of the boards is given as 91  cm.

So,

x+( x+3 )+2x≤91

Solve the above equation,

x+( x+3 )+2x≤91 4x+3≤91 4x≤88 x≤22 (1)

The condition for the length of third board is given as,

2x≥( x+3 )+5 2x≥x+8 x≥8 (2)

From equation (1) and (2),

8≤x≤22

Thus, the length of the shortest board should be greater than or equal to 8 but less than or equal to 22.