Say I have three amounts $A$, $B$ and $C$. And a set of conversions between them $K_{A->B}$, $K_{B->A}$ and $K_{B->C}$. The conversions denote what fraction and at what efficiency they convert between the to amounts in the system, so for example we could have:
$A = 100$
$B = 150$
$C = 0$
$K_{A->B}$ converts 0.2 of A to B at an efficiency of 1
$K_{B->A}$ converts 0.1 of B to A at an efficiency of 1.2
$K_{B->C}$ converts 0.3 of B to C at an efficiency of 0.5
Given that the conversions are cyclic like above, what method could I use to find the final value of A, B and C after conversion?
PS. As I really don't know in which direction to look for a solution to this - I'm not at all proficient at math - please help me tag this question appropriately.