Fraction Word Problem. Wasn't covered in lecture or book.

Question

I bought a length of rope at Lowe's. I used a third for something. I then used a fourth of the remaining length of rope for something. I'm left with 6 ft. What was the original length?

 

I'm also required to model the problem with a picture/manipulative.

Answer 1

Let x = original length

 

x - (1/3)x - (1/4)[x - (1/3)x] = 6

 

(2/3)x - (1/4)(2/3)x = 6

 

(2/3)x - (1/6)x = 6

 

(4/6)x - (1/6)x = 6

 

(1/2)x = 6        x = 12 feet