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?
What was the length of the second piece? what was the length of the third?
Let x be the length of the first piece.
The second piece is 3 times as long as the first piece, so its length is 3x.
The third piece is 4 times as long as the first piece, so its length is 4x.
The lengths of the three pieces add up to 56 inches, so we have the equation x + 3x + 4x = 56.
Combining like terms, we get 8x = 56.
Dividing both sides by 8, we get x = 7.
Therefore, the length of the first piece is 7 inches.
The length of the second piece is 3x = 3 * 7 = 21 inches.
The length of the third piece is 4x = 4 * 7 = 28 inches.