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Math Help - [SOLVED] Pre-Calc applications of equations

  1. #1
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    [SOLVED] Pre-Calc applications of equations

    Hi, I need help on this word problem:

    You have already invested 550$ in a stock with an annual return of 11%. How much of an additional 1100 should be invested at 12% and how much at 6% so that the total return on the entire 1650$ is 9%

    I tried to set up my equations as (550 times .11) + (.12x times 1100) + (.06y times 1100) = (1650 times .09)
    and x + y = 1100

    I am wondering if i am going in the right direction. The answer in the book says 366.67 at 12% and 733.33 at 6% but i tried to work my math and i got nowhere close to that answer.

    can anyone help please?
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  2. #2
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    Hello, soccer49!

    You're on the right track, but you put "too much" in your equations.


    You have already invested $550 in a stock with an annual return of 11%.
    How much of an additional $1100 should be invested at 12% and how much at 6%
    so that the total return on the entire $1650$ is 9% ?

    Let x = amounted invested at 12%.
    Let y = amount invested at 6%.

    Then: . x + y \:=\:1100 .[1]



    $550 at 11% returns $60.50 in interest.

    x dollars at 12% returns 0.12x dollars in interest.

    y dollars at 6% returns 0.06y dollars in interest.

    The total interest is: . 60.50 + 0.12x + 0.06y
    . . and we want this to be equal to 9% of $1650 = $148.50

    There is our equation: . 60.50 + 0.12x + 0.06y \:=\:148.50

    Multiply by 100: . 6050 + 12x + 6y \:=\:14850 \quad\Rightarrow\quad 12x + 6y \:=\:8800 .[2]


    Solve the system of equation.

    \begin{array}{cccccccc}\text{Multiply {\color{blue}[1]} by -6:} & \text{-}6x - 6y &=& \text{-}6600 \\ \text{Add {\color{blue}[2]}:} & 12x + 6y &=& 8800 \end{array}

    And we get: . 6x \:=\:2200 \quad\Rightarrow\quad x \:=\:\frac{2200}{6} \quad\Rightarrow\quad\boxed{ x\:\approx\:\$366.67}

    Substitute into [1]: . 366.67 + y \:=\:1100\quad\Rightarrow\quad \boxed{y \:=\:\$733.33}

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  3. #3
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    Thank you very much, yes that would make sense, i am just not very good at setting up the equations.
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