Consider a hypothetical eutectic phase diagram for metals A and B that is similar to that for the lead-tin system (Figure 9.8). Assume that:

(1) α and β phases exist at the A and B extremes of the phase diagram, respectively;

(2) The eutectic composition is 36 wt% A-64 wt% B;

(3) The composition of the α phase at the eutectic temperature is 88 wt% A-12 wt% B. Determine the composition of an alloy that will yield primary β and total β mass fractions of 0.367 and 0.768, respectively.