Acetone can be recovered from a carrier gas by dissolving it in a pure water stream in a unit called an absorber$.$ In the flowsheet shown below, $200lb\frac{m}{h}$ of a stream containing $20\%$ acetone is treated with $1000l\frac{b}{h}$ of a pure water stream to yield an acetone$-$free overhead gas and an acetone$-$water solution. Assume no carrier gas dissolves in the water.

a$)$ Determine how many independent stream variables and material balances there are in the problem

b$)$ Write out all the material balance equations

c$)$ Calculate all unknown stream variables.