# plz need help solving equations

• Dec 4th 2006, 10:41 PM
gracy
plz need help solving equations
• Dec 5th 2006, 04:48 AM
OReilly
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\$.