A chemical plant produces $\backslash (10,000\backslash$mathrm$\{$lb$\}\_\{\backslash$mathrm$\{$m$\}\}/\backslash$mathrm$\{$hr$\}\backslash )$ of a mixture that contains $60$ weight percent toluene and $40$ weight percent isopropyl alcohol. It is desired to utilize cross$-$current extraction at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to remove the alcohol, using pure water as a solvent. A mass of water equal to $80$ percent of the weight of the feed stream to each stage is fed to each stage. How many stages will be needed to reduce the alcohol concentration in the raffinate to $5$ weight percent? If all of the solvent streams are mixed together, what is the alcohol concentration in water?