# Math Help - plz need help solving equations

1. ## plz need help solving equations

2. 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} 32x + 23y = 10100 \\ 1.20x + 1.40y = 540 \\ \end{array} $ 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} \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 $y$ in first equation: $\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\$.