Let the cost of a game cartridge be x.

Let the cost of a toy car be y.

Then the total cost is

mx + ny = 1615

where m is the number of cartridges bought and n is the number of toy cars bought. And we know that n = 3m, so

mx + 3my = 1615

Now, the cost of a game cartridge is $15 more than the cost of a toy car, so

x = y + 15:

m(y + 15) + 3my = 1615

The total cost of the toy cars, 3my, is $425 more than the total cost of the of the game cartridges, m(y + 15), so:

3my = m(y + 15) + 425

So we now have two equations and two unknowns:

m(y + 15) + 3my = 1615 ==> 4my + 15m = 1615

3my = m(y + 15) + 425 ==> 2my - 15m = 425

Multiply the bottom equation by 2:

4my + 15m = 1615

4my - 30m = 850

Now subtract the bottom equation from the top:

(4my + 15m) - (4my - 30m) = 1615 - 850

45m = 765

m = 17.

Now put m = 17 into one of our two equations. I'll pick on the bottom one again:

2my - 15m = 425

2(17)y - 15(17) = 425

34y - 255 = 425

34y = 680

y = 20

Thus

x = y + 15 = 20 + 15 = 35

So a game cartridge is $35.

-Dan