Problem $3.(15$ points$)$

Three polystyrene batches $($A$,$ B$,$ C$)$ were mixed to produce $50,000g$ polystyrenes. The weight$-$

average molecular mass $(M_w)$ of mixed polymer was $250,000\frac{g}{m}ol$ and PDI was $3\mathrm{.}65$

$(1)$ Calculate the number$-$average molecular weight $(M_n)$ of $A,B,C$ and mixed polymers

$(5$ points$)$

$(2)$ Calculate the weights of $A,B,$ and $C$ in the mixed polystyrenes $(10$ points$)$