I need to solve multiple equations that share variables

I need to be able to solve multiple equations that share variables, or
come up with a best fit.  For instance

A + D + C + F = 100
D + R + F + M = 100
D + R + Z + Q + N = 100

I need to be able to calculate a best fit solution for this.  Is this
a really a problem best solved by a linear best fit approach or
something else?  I've been able to find little that references a
problem such as this. 

Any help would be greatly appreciated.

Thanks!
Jon