$2.(10$ pts$)$ A hypothetical A$-$B alloy of composition $55$ wt$\%$B$-45$ wt$\%$ A at some temperature is found to consist of mass fractions of $0\mathrm{.}5$ for both a and B phases. If the composition of the B phase is $90$ wt$\%$ B $-10$ wt$\%$ A$,$ what is the composition of the a phase?