A solid mixture we're processing contains $28\%$ oil, $60\%$ component X$,$ and $12\%$ benzene. The feed rate is $2\mathrm{.}5$ tons$/$hr$.$ A $1\mathrm{.}25$ tons$/$hr of fresh solvent containing $99\mathrm{.}5\%$ benzene and only $0\mathrm{.}5\%$ oil by weight into the last stage. In each stage, we assume $615$ kg$/$hr of benzene is retained in the solid leaving. The final leftover solid exiting the last stage should only contain $1\mathrm{.}5\%$ oil.

a$.$ Determine the minimum number of ideal stages required to achieve the desired outcome.

b$.$ Calculate the percentage of oil in the solid leaving and liquid leaving from each stage