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?

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(52800)   (Show Source): You can put this solution on YOUR website!
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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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Peter = x = . Next, Paul = , which implies Simon = = = = 2x-90. Total money equation Peter + Paul + Simon = 825 x + + (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 = = = 240 dollars; Simon had 2x-90 = 2*225-90 = 360 dollars. CHECK. 225 + 240 + 360 = 825 dollars, total. ! Correct !

Solved.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
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
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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
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J + 5S/3 = 825
S for J
S/2 + 45 + 5S/3 = 825
13S/6 = 780
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Solve for S, then for J, etc
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

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

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