SOLUTION: The number 100 is separated into two parts such that if 1/3 of one part is subtracted from 1/4 of the other, the difference is 18. Find the two parts.

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Question 1152888: The number 100 is separated into two parts such that if 1/3 of one part is subtracted from 1/4 of the other, the difference is 18. Find the two parts.
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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Let x be the length of one part; then the length of the other part is (100-x).


Next, write the equation from the condition


    %281%2F4%29%2A%28100-x%29%29 - %281%2F3%29x = 18.


Multiply by 3*4 = 12 both sides


    3*(100-x) - 4x = 12*18.


Simplify


    300 - 3x - 4x = 216 - 300

    -7x = -84

     x = %28-84%29%2F%28-7%29 = 12.


ANSWER.  The parts are 12 and 100-12 = 88.


CHECK.  %281%2F4%29%2A88 - %281%2F3%29%2A12 = 22 - 4 = 18.    ! Correct !

Solved.