Single$-$Stage Extraction with Unknown Composition. A feed mixture weighing $200$ kg of unknown composition containing water, acetic acid, and isopropyl ether is contacted in a single stage with $280$ kg of a mixture containing $40$ kg wt $\%$ acetic acid, $10$ wt$\%$ water, and $50$ wt$\%$ isopropyl ether. The resulting raffinate layer weighs $320$ kg and contains $29\mathrm{.}5$ wt$\%$ acetic acid, $66\mathrm{.}5$ wt$\%$ water, and $4\mathrm{.}0$ wt$\%$ isopropyl ether. Determine the original composition of the feed mixture and the composition of the resulting extract layer. Use equilibrium data from Appendix A$\mathrm{.}3$