Question

1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?

Answer 1

To solve the exercise, it is easier to make a drawing, like this

So, you have

`\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}`

Now solving

`\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}`
`\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ (10y)/(10)=(100)/(10) \\ y=10\text{ ft} \end{gathered}`
`\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}`
`\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}`

Therefore, the length of the longest piece is 60ft.