A 56-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces
what was the length of the first piece?
Let x be the length of the first piece.
The second piece is 3 times as long as the first piece, so it measures 3x.
The third piece is 4 times as long as the first piece, so it measures 4x.
The total length of the three pieces is x + 3x + 4x = 8x.
So, 8x = 56 inches.
Hence, the length of the first piece x = 56 inches / 8 = <<56/8=7>>7 inches. Answer: \boxed{7}.