If I wanted to find the value of Cin for the following equation:

*Cin* = *a* *P* *Cout* – (*a* – *k*) *Cin* + *Q* / *V*

Where Cin and Cout are the indoor and outdoor concentrations and the other parameters are as follows;

Cout = 15

*P* = 1

*a* = 1.2

*k* = 1.19

*Q *= 1.4

*V = 2.5*

How C_{in}$ occurs in two places in the equation

\(\displaystyle C_{in}\) occurs in two places in the equation

\(\displaystyle C_{in}= a P C_{out}- (a- k)C_{in}+ Q/V\)

so put them together- add \(\displaystyle (a- k)C_{in}\) to both sides:

\(\displaystyle C_{in}+ (a- k)C_{in}=a P C_{out}+ Q/V\(\displaystyle

Factor out \(\displaystyle C_{in}\) on the left

\(\displaystyle (1+ a- k)C_{in}= a P C_{out}+Q/V\)

Divide both sides by 1+ a- k

\(\displaystyle C_{in}= \frac{a P C_{out}+ Q/V}{1+a- k}\)\)\)