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Math Help - Having trouble getting started on a word problem involving dual APR's

  1. #1
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    Having trouble getting started on a word problem involving dual APR's

    the question is: "Cathy just won $10,000 in the Oregon state lottery. She wants to put some of the money in an account where it is accessible and to commit the rest to a long-term investment. She has been considering a savings account that has been paying an annual percentage rate (APR) of 2.64% and a mutual fund that has been paying an APR of 8.9%. At the end of one year, Cathy hopes to earn $750. How much money must she invest in each type of account?"

    i have manually figured out that $7763.51 must be invested in the 8.9% mutual fund, and $2236.49 must be invested in the 2.64% saving account to yield a profit of $750 on $10,000. The problem is I sort of just ballpark guessed one variable to i narrowed down, and then fine tuned. What would be a systematic and intelligent approach to this problem? thank you
    Last edited by mr fantastic; October 21st 2010 at 04:52 AM. Reason: Edited title.
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  2. #2
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    x = amount invested @ 2.64%; then 10000-x = amount @ 8.9%
    .0264x + .089(10000 - x) = 750
    Solve for x
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  3. #3
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    thx!

    thank you so much for pointing me in the right direction!
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