For alloys of two hypothetical metals A and B, there exist an α, A-rich phase and a β, B-rich phase. From the mass fractions of both phases for two different alloys provided in the following table (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for the alpha phase at this temperature.

Alloy Composition Fraction alpha phase Fraction beta phase
60 wt% A - 40 wt% B 0.60 0.40
30 wt% A - 70 wt% B 0.12 0.88