Engineers Sophia and Giles are modifying a process to make concentrated apple cider starting from a slurry. A slurry is a mixture of solids in a liquid that can nomally be pumped. A slury made with apples having a mass fraction of $0\mathrm{.}422$ and the balance water is fod to a juicer at a rate of $27\mathrm{.}3k\frac{g}{m}in.$ Seventy percent of the apples entering the juicer leave as part of the solid waste stream $($containing apples and water$).$ The primary product from the juicer is cider $(34\mathrm{.}5$wit apples and $65\mathrm{.}5wt\%$ water$).$ The cider is sent to an evaporator where concentrate$-$apple concentration increases to $50\mathrm{.}7$ wi$\%-$is produced along with a stream of pure water that is recycled. The pure water strearn leaving the evaporator is mixed with fresh water entering the process. The combined water stream mixes with pristine apples entering the process to create the slurry. Determine the following three unknowns.

Mass fraction of apple in the solid waste $=$

Total flow rate of the concentrate $=k\frac{g}{m}in$

Flow rate of pure water entering the overall system $=k\frac{g}{m}in$