Question

A rope is 60in in length and must be cut into two pieces. If one piece must be twice as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary

Answer 1

Variables

• x: length of one of the pieces, in inches

,

• y: length of the other piece, in inches

The addition of both pieces makes the original rope which is 60 inches long. Then:

x + y = 60 (eq. 1)

If one piece must be twice as long as the other, then:

x = 2y (eq. 2)

Substituting equation 2 into equation 1:

2y + y = 60

Combining similar terms:

3y = 60

Dividing by 3 at both sides of the equation:

`\begin{gathered} (3y)/(3)=(60)/(3) \\ y=20 \end{gathered}`

Substituting this result into equation 2:

x = 2y

x = 2*20

x = 40

One of the pieces must be 40 in long and the other one must be 20 in long