A water sample contains: $23m\frac{g}{L}N{a}^{+},10m\frac{g}{L}C{a}^{2+},15m\frac{g}{L}M{g}^{2+},35m\frac{g}{L}Cl,16m\frac{g}{L}S{O}_4^{2,},$ and $9m\frac{g}{L}N{O}_3^{-}.$

a$.$ Calculate the hardness of this water $($in $m\frac{g}{L}$ as $CaC{O}_3).$ Is this water classified as soft, moderately hard, hard or very hard?

b$.$ Calculate the concentration $($in $m\frac{g}{L})$ of total dissolved solids $($TDS$)$ in this water sample. This problem came from an old FE exam!!