# SOLUTION: Brian takes an 81 inch piece of rope and cuts it three times. Each time he cuts the rope, he cuts off and discards the same fraction of the remaining length. When he is finished,

Algebra ->  Algebra  -> Percentage-and-ratio-word-problems -> SOLUTION: Brian takes an 81 inch piece of rope and cuts it three times. Each time he cuts the rope, he cuts off and discards the same fraction of the remaining length. When he is finished,      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Word Problems: Problems on percentages, ratios, and fractions Solvers Lessons Answers archive Quiz In Depth

 Question 260050: Brian takes an 81 inch piece of rope and cuts it three times. Each time he cuts the rope, he cuts off and discards the same fraction of the remaining length. When he is finished, the piece of rope is 3 inches long. Which fraction represents the amount of rope removed in each of the three cuts? The answer is 2/3, but I have not a clue why. Answer by dabanfield(803)   (Show Source): You can put this solution on YOUR website! Brian takes an 81 inch piece of rope and cuts it three times. Each time he cuts the rope, he cuts off and discards the same fraction of the remaining length. When he is finished, the piece of rope is 3 inches long. Which fraction represents the amount of rope removed in each of the three cuts? The answer is 2/3, but I have not a clue why. Let x be the common fraction removed with each cut. Then after the first cut the amount of rope left is 81 - x*81 After the second cut then we have: (81-X*81) - x*(81-x*81) After the last cut we have: (81-x*81) - x*(81-x*81) - x*((81-x*81) - x*(81-x*81)) Expanding this we have: 81*(1-x-x+x^2-x+x^2+x^2-x^3) = 3 81*(1-3x+3x^2-x^3) = 3 1-3x+3x^2-x^3 = 3/81 = 1/27 (-x+1)^3 = 1/27 -x+1 = 1/3 x = 1-1/3 = 2/3