please help me asap

Question

a 12 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 3 times as long as the first piece. if x represents the length of the first piece, find the lengths of all 3 pieces

Answer 1

Since there are 3 pieces , we need to create expressions for each piece and add the expressions for a sum of 12 inches.

If the length of the first piece is x, then the length of the second will be 2x (or twice as long). The length of the third piece can be represented with 3x (or 3 times as long as the first).

The sum will then be:

x + 2x + 3x = 12

Now solve this equation by combining like terms and using inverse operations:

x + 2x + 3x = 12

6x = 12

6x/6 = 12/6

x= 2 inches

The first piece is 2 inches long.

The second piece will be 2 * 2 or 4 inches long.

The third piece will be 3 * 2 or 6 inches long.

The sum is 12 inches : 2 + 4 + 6 = 12