Question

A man wants to cut three lengths from a single piece of cloth 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 piece of cloth if the third piece is to be al least 5 cm longer than the second.

Answer 1

Let the length of the shortest piece be x cm. Then, second length = (x +3) cm and third length = 2x cm.

$\therefore x+(x+3)+2x\le 91and2x\ge (x+3)+5$

$\Rightarrow 4x+3\le 91and2x\ge (x+3)+5$

$\Rightarrow 4x+3\le 91and2x\ge x+8$

$\Rightarrow 4x\le 91-3and2x-x\ge 8$

$\Rightarrow 4x\le 88andx\ge 8$

$\Rightarrow x\le 22andx\ge 8$

$\Rightarrow 8\le x\le 22$.
Hence, the length of the shortest piece is to be greater than or equal to 8 but less than or equal to 22.