Answer:
3 pieces from each board
Explanation:
Givens
12 pieces of wood each 10 1/2 feet long
required: each piece will produce x number of wood 3 1/4 feet long.
Formula
number of pieces = 10 1/2 - x * 3 1/4 x is an integer.
Solution
The formula must produce a length that is less than 10 1/2.
The only way I can think to do this is by guessing until you get a number greater than 10 1/2 and then subtract 1 from that value of x.
Let x = 4
number of pieces = 10 1/2 - 4 * 3.25
number of pieces = 10 1/2 - 13
number of pieces = - 2 1/2 The board is too short to give 4 pieces each one of which is 3 1/4. You would need a board that is 2 1/2 feet longer.
4 is too many. So try 3
number of pieces = 10 1/2 - 3 * 3 1/4
number of pieces = 10 1//2 - 9 3/4
number of pieces = 3/4 The board will produce 3 pieces that are 3 1/4 feet loong. 3/4 of a foot is waste.
Each board produces 3 pieces
There are 12 boards
Therefore 3 * 12 = 36 pieces