P$1.$ After the fresh feed solution of $10\%$ trisodium phosphate $(N{a}_{3}P{O}_4)$ by mass is mixed with the recycle stream, it enters an evaporator and its water is removed until its concentration becomes $34\%N{a}_{3}P{O}_4$ by mass. This concentrated solution obtained is cooled to $20C$ in a crystallizer and $100kg$ of $N{a}_{3}P{O}_4*12H_{2}O$ crystals are obtained per hour. While $10\%$ of the saturated solution coming out of the crystallizer is thrown out for cleaning purposes as purge stream, the remaining part is recycled and mixed into the fresh feed stream fed to the system. Accordingly, calculate the following;

a$)$ Mass of fresh feed sent to the system per hour,

b$)$ The mass of the waste stream thrown out for cleaning purposes as purge stream,

c$)$ Calculate the mass of evaporated water.

Note: The solubility of trisodium phosphate in $20C$ water is $11$kgNaP$\frac{O_4}{100}kg{H}_{2}O.$