For alloys of two hypothetical metals A and $B,$ there exist an $,A-$rich phase and a $,$ B$-$rich phase.

From the mass fractions of both phases for two different alloys $($given below$),$ which are at the same temperature, determine the composition of the phase boundary $($or solubility limit$)$ for the following:

$\backslash$table$[[$Alloy Composition,$\backslash$table$[[$Fraction$],[$ Phase$]],\backslash$table$[[$Fraction$],[$ Phase$]]],[60$wt$\%$A$-40$ wt$\%$ B$,0\mathrm{.}56,0\mathrm{.}44],[30$wt$\%$A$-70$wt$\%$B$,0\mathrm{.}15,0\mathrm{.}85]]$