Thread: Single values vs set of values in an equation

I'm not entirely sure where this should go, so if this is in the wrong forum I apologize and would ask a moderator to please move to the correct forum.


What I have is 3 sets of values, A, B, and C, with 10 values in each set, and they each go through the equation B^2/(A*C) = D, such that B1^2/(A1*C1) = D1, etc. I would like to know how putting the total of the set through the equation would change things. B, C, and D can be summed to find the total of the set (Btotal, Ctotal, Dtotal), however A is a rate that depends on C, such that the total of the set is going to be sum(Ai*(Ci/Ctotal)) = Atotal. Should Btotal^2/(Atotal*Ctotal) = Dtotal? If not, is there a relationship between Atotal, Btotal, and Ctotal that accounts for the difference?

No, it shouldn't. The problem is that B^2 and A*C are not linear and it is only linear functions that preserve sums. For example, (A+ B)^2= A^2+ 2AB+ B^2, NOT "A^2+ B^2". (A+ C)(B+ D)= AB+ AC+ BC+ BD, not AB+ CD.