A 28 -inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is four times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
What is the length of the first piece?
x + 2x + 4x = 28
Solve for x, then 2x, then 4x.
Let's set up the problem.
We are given that the second piece is twice as long as the first piece and the third piece is four times as long as the first piece. We can represent the length of the first piece as "x".
So, the second piece would be 2 times the length of the first piece, which is 2x.
The third piece would be 4 times the length of the first piece, which is 4x.
Now, according to the problem, the sum of the lengths of the three pieces should equal the length of the original 28-inch board.
Therefore, we have the equation: x + 2x + 4x = 28
Adding like terms, we have 7x = 28.
Dividing both sides of the equation by 7, we get x = 4.
So, the length of the first piece is 4 inches.
To find the lengths of the second and third pieces, we substitute x = 4 back into the equations we derived.
The second piece: 2x = 2 * 4 = 8 inches
The third piece: 4x = 4 * 4 = 16 inches
Therefore, the lengths of the three pieces are:
First piece: 4 inches
Second piece: 8 inches
Third piece: 16 inches