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Feet-Inch Transpose (Posted on 2013-12-06) Difficulty: 4 of 5
(A) Ben called ahead by telephone and ordered a length of rope which is in integer feet and inches (that is, lengths like 3 feet and 5 inches NOT lengths like 3 feet and 5.5 inches. Also, lengths like 3 feet and 34 inches are untenable.)

When he picked it up, he found that the clerk had wrongly written the order by interchanging the feet and inches. As a result the rope was only 30% of the length he ordered.

What length did he originally order and what length did he get?

(B) If Ben had got p% of the length he ordered, then for what integer values of p from 1 to 100 inclusive are each of the length of the rope he ordered and the length of the rope he received in integer feet and inches?

No Solution Yet Submitted by K Sengupta    
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Solution Extra credit? (spoiler) | Comment 1 of 7

  Let x = original feet and y = original inches

  .3*(12x + y) = 12y + x
    simplifies to
  9y = 2x

  The only positive integers less than 12 are x = 9, y = 2

  So, he ordered 9' 2" (110 inches) and got 2' 9" (33 inches)


  (p/100)*(12x + y) = 12y + x
  p = 100*(12y + x)/(12x + y)

  Using Excel to check all 121 {x,y} combinations finds
  p = 30, 56 and 100 all work (requested answer)
  p = 160, 225, 485, and 550 (extra credit?)


  Posted by Steve Herman on 2013-12-06 15:32:05
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