At the beginning of last year, you purchased Beta Bank and Zeta Functions. The Beta Bank shares cost you $$16$ per share and paid $20\%$ in dividends for the year, while Zeta Functions shares cost you $$16$ per share and paid $15\%$ in dividends for the year. If you invested a total of $$11,200$ and earned $$1,840$ in dividends at the end of the year, how many shares of each company did you purchase?