Oil is extracted from halibut liver using ether in the countercurrent extraction system. The fish to be extracted fed into the extractor contains $100lb$ of inert and $4\mathrm{.}3$ gallons of oil. $95\%$ of the oil is extracted and separated with the upper stream, and the oil rate in this stream is $0\mathrm{.}65.$ Data regarding the solution retained by the inert leaving the lower stream are given in the table. Pure ether is fed to the system with countercurrent as a solvent. The oil rate in the lower stream leaving the system is $0\mathrm{.}055.$ Based on the above information:

a$)$ Calculate the amount of ether to be fed to the extractor.

b$)$ How many stages are needed? Calculate by drawing a graph.

$\backslash$table$[[$gal solution$/1$ lb inert,gal oil$/$gal solution$],[0,035,0,035],[0,042,0,042],[0,05,0,05],[0,058,0,058],[0,068,0,068],[0,081,0,081],[0,099,0,099],[0,120,0,120]]$