Consider the hypothetical eutectic phase diagram for metals A and $B,$ which is similar to that

for the lead$-$tin system $($see your text$),$ Assume that:

$($i$)$ and $$ phases exist at the A and $B$ extremities of the phase diagram,

$($ii$)$ The eutectic composition is $47wt\%B-53wt\%A,$

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

Determine the composition of an alloy that will yield primary of $$ and total $$ mass fraction of

$0\mathrm{.}356$ and $0\mathrm{.}693,$ respectively.