# Formula derivation, algebra

by raintrek
Tags: algebra, derivation, formula
 P: 76 I'm trying to derive a formula but can't seem to work the algebra. I need to combine these two: $$V_{1}p_{1} + V_{2}p_{2} = N$$ $$V_{1} + V_{2} = V$$ to get this: $$\frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}}$$ where $$p = N/V$$ If anyone could show me the steps that would be a huge help. Thanks in advance!
 HW Helper P: 2,618 Were you trying to obtain $$\frac{V_{1}}{V} = \frac{p-p_{2}}{p_{1}-p_{2}}$$ instead? With $$\frac{V_{1}}{V} = \frac{p-p_{1}}{p_{2}-p_{1}}$$, I got $$V_{2}p_{1} + V_{1}p_{2} = N$$ instead.
 P: 76 Dang, that will teach me to copy and paste! I'm sorry, Defennder, here's the correct expressions: $$\frac{V_{2}}{V}=\frac{p-p_{1}}{p_{2}-p_{1}}$$
HW Helper
P: 2,618

## Formula derivation, algebra

$$V_{1}p_{1} + V_{2}p_{2} = N$$
$$(V-V_{2})p_{1} + V_{2}p_{2} = pV$$
Rearraging to get:
$$(p_{2}-p_{1})V_{2} = (p - p_{1})V$$

From here you just rearrange the terms and you'll get the answer.

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