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- Dec 4th 2006, 10:41 PMgracyplz need help solving equations
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- Dec 5th 2006, 04:48 AMOReilly
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 $32 and 300 shares of 23$.