$A$ 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?

(N/A) Let the length of the shortest piece be $x \, cm$. Then,the lengths of the second and third pieces are $(x+3) \, cm$ and $2x \, cm$ respectively.
Since the three lengths are cut from a single board of length $91 \, cm$:
$x + (x+3) + 2x \leq 91$
$4x + 3 \leq 91$
$4x \leq 88$
$x \leq 22$ ...... $(1)$
Also,the third piece is at least $5 \, cm$ longer than the second piece:
$2x \geq (x+3) + 5$
$2x \geq x + 8$
$x \geq 8$ ...... $(2)$
From $(1)$ and $(2)$,we obtain:
$8 \leq x \leq 22$
Thus,the possible length of the shortest board is greater than or equal to $8 \, cm$ but less than or equal to $22 \, cm$.