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  1. MHB Craftsman

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    #1
    1. A trust fund has invested \$8000 at 6% annual interest.
    How much additional money should be invested at
    8.5% to obtain a return of 8% on the total amount
    invested?

    my solution,

    let
    $n=$amount invested @ 8.5%

    $0.06(8000)+0.085n=0.08(8000+n)$

    $480+0.085n=640+0.08n$

    $0.085n-0.08n=640-480$

    $n=32,000$

    \$32,000 is the addtional money should be invested at 8.5%. is this correct?

    2. A businessman invested a total of \$12,000 in two ven-tures. In one he made a profit of 8% and in the other he
    lost 4%. If his net profit for the year was $120, how
    much did he invest in each venture?

    in this problem i don't know how will i represent the amount invested in the other venture. please help. thanks!

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  3. Pessimist Singularitarian
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    MarkFL's Avatar
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    #2
    1.) Correct.

    2.) Let $x$ represent the first investment amount and $y$ represent the other. So we know:

    $ \displaystyle x+y=12000$

    And we also know:

    $ \displaystyle 0.08x-0.04y=120$

    which I would rewrite as:

    $ \displaystyle 2x-y=3000$

    Now, add the two equations to eliminate $y$, then solve for $x$, then use this value of $x$ in either of the two equations to determine $y$.

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