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Math Help - Investing her bonus

  1. #1
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    Investing her bonus

    Please help me find the equation to work out this problem. Your help is much appreciated.

    Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?
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  2. #2
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    To learn how to set up and solve this sort of exercise, try here.

    Then:

    . . .invested:
    . . . . .at 4%: x
    . . . . .at 2.25%: 33,000 - x

    . . .interest:
    . . . . .at 4%: 0.04x
    . . . . .at 2.25%: ??(33,000 - x)

    Complete the table. Sum the two interest expressions, and set equal to the given total. Then solve the linear equation. Back-solve for the required values.
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  3. #3
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    Quote Originally Posted by stapel View Post
    To learn how to set up and solve this sort of exercise, try here.

    Then:

    . . .invested:
    . . . . .at 4%: x
    . . . . .at 2.25%: 33,000 - x

    . . .interest:
    . . . . .at 4%: 0.04x
    . . . . .at 2.25%: ??(33,000 - x)

    Complete the table. Sum the two interest expressions, and set equal to the given total. Then solve the linear equation. Back-solve for the required values.
    Thanks for the link. I set up a table. The 2.25% threw me a bit. It took me a few attempts before I realized I just needed to set 2.25% to just 0.02, not 0.0225, nor 0.023.

    Out of the table, I ended up working out the following:
    0.04+0.02(33000-x)=970
    0.04x+660-0.02x=970
    660+0.02x=970
    0.02x=310
    x=15500

    y=33000-15500=17500
    y=17500

    So she invested $15,500 at the 4% rate.
    She invested $17,500 at the 2.25% rate.

    Does this look correct?
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  4. #4
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    The answer to any "solving" exercise can be checked by plugging it back into the original question. So plug the values into the "simple interest" formula, and verify that the interest amounts sum to the correct value.
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  5. #5
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    Quote Originally Posted by dkpeppard View Post
    It took me a few attempts before I realized I just needed to set 2.25% to just 0.02, not 0.0225, nor 0.023.
    Your answer is incorrect.
    HOW in heck did you realise that?! 2.25% is .0225 (nothing else!).
    .04x + .0225(33000 - x) = 970
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  6. #6
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    Quote Originally Posted by Wilmer View Post
    Your answer is incorrect.
    HOW in heck did you realise that?! 2.25% is .0225 (nothing else!).
    .04x + .0225(33000 - x) = 970
    When I multiply 0.0225*33000 I get 742.50. For some reason the decimal was throwing me off, so I thought I needed to round the interest up from 0.0225 to 0.02 to get an even value of 759.
    Last edited by dkpeppard; November 12th 2009 at 11:23 AM. Reason: clarified interest rounded to 0.02
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  7. #7
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    Ok, I reworked the problem and got the following.

    0.04+0.0225(33000-x)=970
    0.04x+742.50-0.02x=970
    742.50+0.0175x=970
    0.0175x=227.50
    x=13000

    y=33000-13000=20000
    y=20000

    So,
    For the 4% rate she invested $13000.
    For the 2.25% rate she invested $20000.

    Thank you for help guide me. Not sure why I got so hung up on the decimal in the problem last night.
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  8. #8
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    C'est correct. Bien fait!
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