Question

To do A rope trick a magician need to cut a piece of rope so that one piece is 1/3 the length of the other piece if she begins with 2 2/3 feet of rope what will be the length of the two pieces of rope

Answer 1

`(2)/(3)ft\text{ and 2 ft}`

Step-by-step explanation

Let the length of the second piece of rope be x.

This means that the length of the first piece of rope is:

`\begin{gathered} (1)/(3)\cdot x \\ (1)/(3)x \end{gathered}`

She begins with 2²/₃ feet of rope. The length of the first and second pieces must sum up to 2²/₃ feet.

Therefore:

`x+(1)/(3)x=2(2)/(3)`

Solve for x in the equation:

`\begin{gathered} 1(1)/(3)x=2(2)/(3) \\ \Rightarrow(4)/(3)x=(8)/(3) \\ \text{Multiply both sides by }(3)/(4)\colon \\ x=(8)/(3)\cdot(3)/(4) \\ x=2\text{ feet} \end{gathered}`

Therefore, the length of the second piece is 2 feet.

This means that the length of the first piece is:

`\begin{gathered} (1)/(3)\cdot2 \\ \Rightarrow(2)/(3)\text{ feet} \end{gathered}`