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 ?

Let the length of the first piece (or the shortest piece) be x cm
   Length of the second piece = (x + 3) cm
Also, the length of the third piece = 2x cm. The maximum length of the board available = 91 cm.
                             ...(i)
Also, the third piece is to be at least 5 cm longer than the second.
                                                           ...(ii)
From (i) and (ii), we have 
Hence, the shortest board (or the first board) can have a minimum length of 8 cm and a maximum length of 22 cm.