How can I derive the formula using algebra for combining two equations?

[raintrek]

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!

 

[Defennder]

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.

 

[raintrek]

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}}

 

[Defennder]

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.