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Tom and Peter have some money. The price of game cartridge is $45. If Tom buys this game cartridge, the ratio of his money left to that of Peter's will be 1:3. However, if Peter buys the game cartridge, the ratio of his money left to that of Tom's is 3:5. How much money does each boy have at first?

 Nov 7, 2021
 #1
avatar+115335 
+1

A please would have helped, but look at it like this

 

\(\frac{T-45}{P}=\frac{1}{3}\qquad and \qquad \frac{P-45}{T}=\frac{3}{5}\)

 

Now solve them simultaneously.

 Nov 7, 2021
 #2
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+1

\( {T - 45 \over p} = {1 \over 3}\)
3(T-45) = P

3T - 135 = P

3T - P = 135 --(1)


 

\( {P - 45 \over T} = {3 \over 5}\)
5(p-45) = 3T

5P=225+3T

5P-3T=225 --(2)

 

Add equation (1) and (2)

3T-P=135            3-P=135

-3T+5P=225      -3+5P=225

------------------

4P=360

  P=360/4=90

Put P=90 in equation (1)

      3T-90=135

        3T=135+90

          T=225/3=75

P=90

T=90

Guest Nov 7, 2021
 #3
avatar+115335 
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Guest, please do not answer over the top of me.

 

I give partial answers for a reason and the asker is always encouraged to ask for more help if required.

 

I do not want this to be just a cheat site. 

 

I want it to be a teaching / help site.  I think that is what most of the answerers here would want.

 

If you want to answer a question in full that is fine,  but choose one, of the many, that does not already have a correct partial answer.

 

Thank you.

 Nov 7, 2021
edited by Melody  Nov 7, 2021
 #4
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+1

No that's me, I want to see if my answer is right.

Guest Nov 7, 2021
 #5
avatar+115335 
0

ok, sorry

You need to identify yourself next time. 

If you become a member that would be the easiest way.  

Plus if you make a good impression your questions will be answered better and quicker. 

 

I have not looked at your answer in any great detail but it looks fine to me.  (I don't have my solution anymore)

Melody  Nov 7, 2021

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