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Thread: plz need help solving equations

  1. #1
    Junior Member
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    plz need help solving equations

    please see attachment file
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  2. #2
    Senior Member OReilly's Avatar
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    Lets say that $\displaystyle x$ is first type of shares and $\displaystyle y$ is second type of shares.

    So you can buy total shares:
    $\displaystyle \$ 32 \cdot x + \$ 23 \cdot y = \$ 10100$

    In order to earn $540 you must set following equation:
    $\displaystyle \$ 1.20 \cdot x + \$1.40 \cdot y = \$ 540$


    So you have systems of equations:
    $\displaystyle \begin{array}{l}
    32x + 23y = 10100 \\
    1.20x + 1.40y = 540 \\
    \end{array}
    $


    We solve first equation for $\displaystyle x$:
    $\displaystyle x = \frac{{10100 - 23y}}{{32}}$

    We susbtitute $\displaystyle x$ in second equation:
    $\displaystyle 1.20(\frac{{10100 - 23y}}{{32}}) + 1.40y = 540$
    $\displaystyle \begin{array}{l}
    \frac{{12120 - 27.6y}}{{32}} + 1.40y = 540 \\
    \frac{{12120 - 27.6y + 44.8y}}{{32}} = 540 \\
    \frac{{12120 + 17.2y}}{{32}} = 540 \\
    12120 + 17.2y = 17280 \\
    17.2y = 5160 \\
    y = 300 \\
    \end{array}
    $

    We susbtitute $\displaystyle y$ in first equation:
    $\displaystyle \begin{array}{l}
    32x + 23 \cdot 300 = 10100 \\
    32x + 6900 = 10100 \\
    32x = 3200 \\
    x = 100 \\
    \end{array}
    $

    So solution is that you have to buy 100 shares of $32 and 300 shares of 23$.
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