Derivation
Suppose an alloy at an equilibrium temperature T consists of c wt% (weight percentage) of element B. Suppose also that at temperature T the alloy consists of two phases, α and β, for which the α consists of a wt% B, and β consists of b wt% B. Let the weight of the α phase in the alloy be so that the weight of the β phase is, where is the total weight of the alloy.
By definition, then, the total weight of element B in the α phase is, while the total weight of element B in the β phase is . Together these two quantities sum to the total weight of element B in the alloy, which is given by . Therefore
By rearranging, one finds that
This final quantity is the weight percentage of the α phase in the alloy.
Read more about this topic: Lever Rule