Question 1152888
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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


    {{{(1/4)*(100-x))}}} - {{{(1/3)x}}} = 18.


Multiply by 3*4 = 12 both sides


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


Simplify


    300 - 3x - 4x = 216 - 300

    -7x = -84

     x = {{{(-84)/(-7)}}} = 12.


<U>ANSWER</U>.  The parts are 12 and 100-12 = 88.


<U>CHECK</U>.  {{{(1/4)*88}}} - {{{(1/3)*12}}} = 22 - 4 = 18.    ! Correct !
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Solved.