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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 4, 2021
 #1
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let x represents the dollars owned by Tom

and y represents the dollars owned by Peter.

Given that, the price of the game cartridge is 

$45.

 If Tom buys the game cartridge, then the

money left to Tom is x−45. and the ratio of

his money and the Peter's is 1:3.

That is, \( {x-45 \over y}={1 \over 3}.\)
\( {x-45 \over y}={1 \over 3}.\) 
3x-135=y

3x-y=135

 

 

 

If Peter buys the game cartridge, then the

money left to Peter is y - 45. and the ratio of

his money and the Peter's is 3:5.

\( {y-45\over x}={3 \over 5}\)

3x=5y-225

x=5/3y-223/3

Substitute (2) in (1),
3x-y=135

3(5/3y-223/5)-y=135

y=90

Substitute y=90 in (2),

x=5/3(90)-225/3

x=75

Therefore, Tom has $75 and Peter has $90 at first.

 Nov 6, 2021

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