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# Help me to solve this problem

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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+0 Answers #1 +1 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