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Math Help - Chinese Math PRoblem

  1. #1
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    Chinese Math PRoblem

    There are 2 piles of coins. One pile contains 8 gold coins and the other 12 silver coins. The 2 piles of coins weigh the same. One coin is taken from each pile and put into the other. It is now found that the pile of mainly gold coins weighs 2 units more than the pile of mainly silver coins. Find the weight of a silver coins and a gold coin.
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  2. #2
    Super Member Aryth's Avatar
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    You can see that there are 7 gold coins and 1 silver coin in one stack, and 11 silver coins and 1 gold coin in another stack, now, if we call the weight of 1 gold coin x and the weight of 1 silver coin y, we get:

    7x + y = 11y + x + 2

    Now, we can combine like terms:

    6x -10y = 2

    And, we also know that 8 gold coins have the same weight as 12 silver coins, so we get:

    8x = 12y

    Which gives us:

    8x - 12y = 0

    Now we have a system of equations:

    6x - 10y = 2
    8x - 12y = 0

    Solve for x and y and you will have the weights of the gold and the silver coins.
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  3. #3
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    I keep getting a negative number
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  4. #4
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    I keep getting a negative number - that cant be right can it?
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  5. #5
    Super Member Aryth's Avatar
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    Notice that you get:

    x = -3 and y = -2

    As answers, but also notice this:

    8x = 12y

    If x and y are -3 and -2, they solve the equation, but now lets assume that x = 3 and y = 2. The equation is still solved, which says that:

    8(-x) = 12(-y)
    -8x = -12y
    8x = 12y

    Which means:

    [8(-x) = 12(-y)] = (8x = 12y)

    So, even though we get negative numbers, they give you the actual answer in positive numbers.

    Using x = -3 and y = -2, we get:

    8(-3) = 12(-2)

    -8(3) = -12(2)

    8(3) = 12(2)

    x = 3, y = 2.
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