A 14 inch board is to be cut into 3 pieces so that the second piece is twice 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
Let's start by assigning the length of the first piece as 'x'.
According to the problem, the second piece is twice as long as the first piece. Therefore, the length of the second piece would be 2x.
Similarly, the third piece is 4 times as long as the first piece. Therefore, the length of the third piece would be 4x.
Now, we have the lengths of all three pieces:
First piece: x
Second piece: 2x
Third piece: 4x
To find the lengths of the three pieces, we can set up an equation based on the given information:
Let x represent the length of the first piece.
According to the given conditions:
- The second piece is twice as long as the first piece: 2x.
- The third piece is four times as long as the first piece: 4x.
The sum of the lengths of the three pieces should be equal to the length of the 14-inch board. Therefore, the equation can be formulated as:
x + 2x + 4x = 14
Simplify the equation:
7x = 14
To solve for x, divide both sides of the equation by 7:
x = 14 / 7
x = 2
Now that we have found the value of x, we can substitute it back into the lengths of the three pieces:
First piece: x = 2 inches
Second piece: 2x = 2 * 2 = 4 inches
Third piece: 4x = 4 * 2 = 8 inches
Therefore, the lengths of the three pieces are 2 inches, 4 inches, and 8 inches, respectively.
x + 2x + 3x + 2 = 14
6x + 2 = 14 (subtract 2 from both sides)
6x = 12 (divide 6 from both sides)
x = 2
x + 2x + 4x = 14
7x = 14
x = 2