Question

A 49-inch board is to be cut into three pieces so that the second piece is twice as long as the first plece 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 is the length of the first piece? What is the length of the second piece? What is the length of the third piece?

Answer 1

three-pieceThe Solution.

Step 1:

We shall express each of the three pieces in terms of x.

First piece: x

Second piece: 2x

Third piece: 4x

Step 2:

We shall write the equation that defines the problem under consideration.

$\begin{gathered} x+2x+4x=49 \\ \text{Collecting like terms, we get} \\ 7x=49 \\ \text{Dividing both sides by 7, we get} \\ x=\frac{49}{7}=7\text{ inches.} \end{gathered}$

Step 3:

We shall obtain the lengths of the three piece of the board by substituting 7 for x as below.

he first piece: x = 7 inches

The second piece = 2x = 2x7 = 14 inches

The third piece = 4x = 4x7 = 28 inches.