John and Angeline are using a filter to remove water from algae, since algae is their favorite health food. They feed a mixture of water and $6\mathrm{.}45$mass$\%$ algae to the filter. The filtrate contain $98\mathrm{.}5$mass$\%$ water and the remainder algae, while the filter cake contains $54\mathrm{.}3$ mass$\%$ algae and water. The component flow rate of the algae in the filter cake is $762k\frac{g}{?}$ day. The densities of water and algae are $998k\frac{g}{m^3}$ and $1010k\frac{g}{m^3},$ respectively.

$($a$)$ Draw and label a process flow diagram by numbering each stream.

$($b$)$ If each stream is labeled with a total mass flow rate and mass fractions, the number of unknown mass flow rates and mass fractions is:

$($c$)$ List the unknown flow rates and fractions.