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Math Help - Investing money at different rates.

  1. #1
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    Investing money at different rates.

    Okay

    Sam has $12,000. He invests this money into a savings account and a bond account. The savings account has an interest rate of 4%, while the bond has a rate of 6%. The total interest he collected at the end of the year was $640. how much did he invest into each account? I've done these multiple times in class but I can't get the formula drilled into my brain.

    i know that
    x+y = 12000
    and .04x + .06y = 640

    x = savings
    y = bond

    so y = 12000 - x

    .04x + .06(12000 - x) = 640
    if i distribute i get..
    .04x + 720 - .06x = 640
    .04x -.06x = -.02x

    -.02x + 720 = 640

    this is where I got lost

    this is where I got lost.
    Last edited by qleeq; November 24th 2009 at 05:39 PM. Reason: edited in more explanation
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  2. #2
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    Quote Originally Posted by qleeq View Post
    Okay

    i know that
    x+y = 12000
    and .04x + .06y = 640

    x = savings
    y = bond
    I would write it as

    x+y = 12000
    and 1.04x + 1.06y = 12000+640

    Now y = 12000-x

    so

    1.04x + 1.06(12000-x) = 12000+640

    now solve for x and in turn find y
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  3. #3
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    Quote Originally Posted by pickslides View Post
    I would write it as

    x+y = 12000
    and 1.04x + 1.06y = 12000+640

    Now y = 12000-x

    so

    1.04x + 1.06(12000-x) = 12000+640

    now solve for x and in turn find y
    why did you change it to 104% when 640 was left the same in the original equation?

    1.04x + 12720 - 1.06x = 12640
    then
    -.02x + 12720 = 12640
    -.02x = -80
    -.02x/-.02 = -80/-.02
    x = 4000
    12000 - 4000 = 8000
    x = 4000, y = 8000

    oh.. thanks lol
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  4. #4
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    Quote Originally Posted by qleeq View Post
    why did you change it to 104% when 640 was left the same in the original equation?
    I don't understand this comment. I changed the 640 to 12000+640, the invested amount plus the interest.
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  5. #5
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    Quote Originally Posted by pickslides View Post
    I don't understand this comment. I changed the 640 to 12000+640, the invested amount plus the interest.
    Well.. it was originally 4% and 6% which are .04 and .06 respectively.
    so how did you get 1.04 and 1.06? just some elaboration on that is that i'm looking for.
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  6. #6
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    1.04 is the mulitplier for a 4% increase on the original investment.

    1.06 is the mulitplier for a 6% increase on the original investment.
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