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# Help me melody

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

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

Guest Nov 7, 2021
#5
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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