$4\mathrm{.}9.$ A feed slurry containing $BaS{O}_4,H_{2}S{O}_4$ and water is washed with water in three stages. The washing takes place in three washer$/$settler tanks such that the washed slurry moves from tank to tank$,$ while the decanted solution $($free of $BaS{O}_4)$ is withdrawn and collected in a common stream. $80\%$ of the $H_{2}S{O}_4$ is removed in each tank. The slurry has a mass fraction of $BaS{O}_4$ of $0\mathrm{.}56.$ The washed $BaS{O}_4$ is dried to remove $90\%$ of the mass of the water $($none of the $H_{2}S{O}_4$ is removed$).$ A sketch of the wash system is shown below. Make a mass balance for the system to determine the flow of water to each tank and the mass fraction of $H_{2}S{O}_4$ in the washed and dried $BaS{O}_4.$