Consider the hypothetical eutectic phase diagram for metals A and B$,$ which is similar to that for the lead$-$tin system, Figure $11\mathrm{.}8.$ Assume that

$[7$ and $$ phases exist at the A and B extremities of the phase diagram, respectively;

$[5.$The eutectic composition is $47wt\%B-53wt\%A$;

$3$ The composition of the $$ phase at the eutectic temperature is $92\mathrm{.}6wt\%B-7\mathrm{.}4wt\%A.$

a$)$ Determine the composition of an alloy that will yield primary $$ and total $$ mass fractions of $0\mathrm{.}356$ and $0\mathrm{.}693,$ respectively. $(5)$

b$)$ what is the mass fraction of eutectic $?(5)$

c$)$ Determine the mass fraction of eutectic microconstituents, $(5)$