Question

A rope is 42 inches long and is cut into two pieces. The first piece is 6 less than 2 times the length of the second piece. How long is each piece of rope?

Answer 1

Length of the first piece = 26 inches

Length of the second piece = 16 inches

Step-by-step explanation:

Let the length of the second piece = x

2 times the length of the second piece =2x

6 less than 2 times the length of the second piece = 2x-6

Then the sum of the lengths

`x+2x-6=42`

First, we solve for x.

`\begin{gathered} 3x=42+6 \\ 3x=48 \\ x=(48)/(3) \\ x=16\text{ inches} \end{gathered}`

The length of the first piece will be:

`\begin{gathered} =2x-6 \\ =2(16)-6 \\ =32-6 \\ =26\text{ inches} \end{gathered}`