1. Convert mixed numbers to improper fractions: $$16\frac{3}{5} = \frac{83}{5}$$, $$17\frac{7}{10} = \frac{177}{10}$$.
2. Find a common denominator (10): $$\frac{83}{5} = \frac{166}{10}$$.
3. Add the fractions: $$\frac{166}{10} + \frac{177}{10} = \frac{343}{10} = 34\frac{3}{10}$$.