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Math Help - plz need help solving equations

  1. #1
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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 x is first type of shares and y is second type of shares.

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

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


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


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

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

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

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