Question 1190609
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Peter, Paul and Simon had $825 altogether. 
1/3 of Peter's money was $15 more than 1/4 of Paul's money. 
Paul had 2/3 as much as Simon. 
How much more money did Simon have than Peter?
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<pre>
    Peter = x

    {{{(1/3)x}}} = {{{(1/4)Paul + 15,

or

    4x = 3*Paul + 180

    Paul = {{{(4x-180)/3}}}.


Next,

    Paul = {{{(2/3)*Simon}}},

which implies


    Simon = {{{(3/2)*Paul}}} = {{{(3/2)*((4x-180)/3)}}} = {{{(4x-180)/2}}} = 2x-90.


Total money equation

    Peter + Paul         + Simon    =   825

      x   + {{{((4x-180)/3)}}} + (2x-90)  =   825

      3x  + (4x-180)     + (6x-270) = 3*825

             3x + 4x + 6x           = 3*825 + 180 + 270

                 13x                =      2925

                   x                =      2925/13 = 225 dollars.


<U>ANSWER</U>.  Peter had 225 dollars;  Paul had  {{{(4x-180)/3}}} = {{{(4*225-180)/3}}} = {{{(4/3)*225-20)}}} = 240 dollars;  Simon had  2x-90 = 2*225-90 = 360 dollars.


<U>CHECK</U>.   225 + 240 + 360 = 825 dollars,   total.    ! Correct !
</pre>

Solved.