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Formula derivation, algebra 
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#1
May308, 10:01 AM

P: 76

I'm trying to derive a formula but can't seem to work the algebra.
I need to combine these two: [tex]V_{1}p_{1} + V_{2}p_{2} = N[/tex] [tex]V_{1} + V_{2} = V[/tex] to get this: [tex]\frac{V_{1}}{V} = \frac{pp_{1}}{p_{2}p_{1}}[/tex] where [tex]p = N/V[/tex] If anyone could show me the steps that would be a huge help. Thanks in advance! 


#2
May308, 10:20 AM

HW Helper
P: 2,616

Were you trying to obtain [tex]\frac{V_{1}}{V} = \frac{pp_{2}}{p_{1}p_{2}} [/tex] instead?
With [tex]\frac{V_{1}}{V} = \frac{pp_{1}}{p_{2}p_{1}}[/tex], I got [tex]V_{2}p_{1} + V_{1}p_{2} = N[/tex] instead. 


#3
May308, 10:53 AM

P: 76

Dang, that will teach me to copy and paste!
I'm sorry, Defennder, here's the correct expressions: [tex]\frac{V_{2}}{V}=\frac{pp_{1}}{p_{2}p_{1}}[/tex] 


#4
May308, 11:03 AM

HW Helper
P: 2,616

Formula derivation, algebra
[tex]V_{1}p_{1} + V_{2}p_{2} = N[/tex]
[tex](VV_{2})p_{1} + V_{2}p_{2} = pV[/tex] Rearraging to get: [tex](p_{2}p_{1})V_{2} = (p  p_{1})V[/tex] From here you just rearrange the terms and you'll get the answer. 


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