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Math Help - system of equations

  1. #1
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    Question system of equations

    ok, here's the question...

    Bechorath bought 3 times as many toy cars as game cartridges. He spent $1615 altogether. A game cartridge costs $15 more than a toy car. The total cost of the toy cars was $425 more than the total cost of game cartridges. Find the cost of a game cartridge.

    I would be gald if u help me.....
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by BlAcK-lIsTeD View Post
    ok, here's the question...

    Bechorath bought 3 times as many toy cars as game cartridges. He spent $1615 altogether. A game cartridge costs $15 more than a toy car. The total cost of the toy cars was $425 more than the total cost of game cartridges. Find the cost of a game cartridge.

    I would be gald if u help me.....
    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
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  3. #3
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    thank u but....

    thanks for helping me but can u explain it in a easier way? i m really bad in maths....thanks a bunch!
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