Assuming Raoult's law to apply to the system $n-$pentane$(1)/$n$-$heptane$(2),$ what are the values of $x_1$ and $y_1$ at $T=55C$ and $P=\frac{1}{2}($P$1$sat$+$P$2$sat$)?$

Antoine Equation:

$ln(Psa\frac{t}{k}Pa)=A-B(\frac{T}{}C)+C$

$\backslash$table$[[$Compound$,n-$pentane,$n-$heptane$],[$A$,13\mathrm{.}7667,13\mathrm{.}8622],[$B$,2451\mathrm{.}88,2911\mathrm{.}26],[$C$,232\mathrm{.}014,216\mathrm{.}432]]$