Three friends, A$,$ B$,$ and C$,$ start a business with investments in the ratio of $2$ : $3$ : $5,$ respectively. A invested $$8,500,$ and all three of them agree to share profits in the ratio of their investments.Round to the nearest cent.

a$.$ Calculate C$\text{'}$s investment.

b$.$ If A$\text{'}$s profit was $$80,000$ in the first year, calculate B$\text{'}$s profit.