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 the length of the shortest board be x cm

Then length of the second board =(x+3) cm length of the third board =2x cm

Now $x+(x+3)+2x\le 91$ and $2x\ge (x+3)+5$

$\Rightarrow 4x+3\le 91$ and $2x-(x+3)\ge 5$

$\Rightarrow 4x\le 91-3$ and $2x-x-3\ge 5$

$\Rightarrow 4x\le 88$ and $x\ge 5+3$

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

Thus minimum length of shortest boards is 8 cm and maximum length is 22 cm.