Question

A man bought a length of rope at the hardware store. He used 1/4 of it to make a bow painter (a rope located at the front of the canoe) for his canoe and then used 1/3 of the remaining piece to tie up a roll of carpet he now has 24 ft of rope left. What was the length of the Rope he had originally purchased?

Answer 1

Answer-

He purchased a rope of 48 ft.

Solution-

Let us assume the length of the rope he had originally purchased was x ft.

He used one-fourth of the x to make a bow, so the rope he used was

$=\dfrac{x}{4}\ ft$

The amount he left with was,

$=(x-\dfrac{x}{4})\ ft$

Then he used one-third of the remaining to tie up a roll of carpet, so the rope he used was

$=(x-\dfrac{x}{4})\dfrac{1}{3}\ ft$

Then he left with 24 ft of rope.

∵ The total amount = Amount used + Amount left

Hence,

$\Rightarrow \dfrac{x}{4}+(x-\dfrac{x}{4})\dfrac{1}{3}+24=x$

$\Rightarrow \dfrac{x}{4}+\dfrac{x}{3}-\dfrac{x}{12}+24=x$

$\Rightarrow \dfrac{x}{4}+\dfrac{x}{3}-\dfrac{x}{12}-x=-24$

$\Rightarrow \dfrac{3x+4x-x-12x}{12}=-24$

$\Rightarrow \dfrac{-6}{12}x=-24$

$\Rightarrow \dfrac{1}{2}x=24$

$\Rightarrow x=24\times 2=48$

Therefore, he purchased a rope of 48 ft.