SOLUTION: 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?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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?      Log On


   

Question 1190609: 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?
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
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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?
~~~~~~~~~~~~~~~ 

    Peter = x

    %281%2F3%29x = .


Next,

    Paul = %282%2F3%29%2ASimon,

which implies


    Simon = %283%2F2%29%2APaul = %283%2F2%29%2A%28%284x-180%29%2F3%29 = %284x-180%29%2F2 = 2x-90.


Total money equation

    Peter + Paul         + Simon    =   825

      x   + %28%284x-180%29%2F3%29 + (2x-90)  =   825

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

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

                 13x                =      2925

                   x                =      2925/13 = 225 dollars.


ANSWER.  Peter had 225 dollars;  Paul had  %284x-180%29%2F3 = %284%2A225-180%29%2F3 = %284%2F3%29%2A225-20%29 = 240 dollars;  Simon had  2x-90 = 2*225-90 = 360 dollars.


CHECK.   225 + 240 + 360 = 825 dollars,   total.    ! Correct !

Solved.



Answer by Alan3354(69443) About Me  (Show Source):
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Johm, Paul and Simon had $825 altogether. 1/3 of John'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 John?
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Changed Peter to John to use initials.
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J + P + S = 825
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1/3 of John's money was $15 more than 1/4 of Paul's money.
J/3 = P/4 + 15
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Paul had 2/3 as much as Simon
P = 2S/3
==================
Sub for P
J + P + S = 825
J + 2S/3 + S = 825
J + 5S/3 = 825
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J/3 = P/4 + 15
J/3 = S/6 + 15
J = S/2 + 45
----
J + 5S/3 = 825
S for J
S/2 + 45 + 5S/3 = 825
13S/6 = 780
----
Solve for S, then for J, etc

Answer by greenestamps(13200) About Me  (Show Source):
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Both responses you have received so far show valid solution methods.

I personally would take some time figuring out how to set up the problem so that I use fractions as little as possible.

(1) Paul had 2/3 as much as Simon:
Paul = 2x; Simon = 3x

(2) 1/3 of Peter's money was $15 more than 1/4 of Paul's money:
I need an expression for 1/4 of Paul's money, which I currently have defined as 2x. I'll change that to 4x to make 1/4 of Paul's money a whole number times my variable x:
Paul = 4x; Simon = 6x

Now 1/3 of Peter's money is $15 more than 1/4 of 4x, which is x:
1/3 of Peter's money = x+15
Peter's money: 3x+45

Now we have "nice" expressions for each person's money:
Paul = 4x; Simon = 6x; Peter = 3x+45

The total is $825:
4x+6x+3x+45=825
13x=780
x=60

Paul: 4x=240
Simon: 6x=360
Peter: 3x+45=225

ANSWER: (how much more money Simon had the Peter): $360-$225=$135