Ms$.$ Hardin invested $$40,000$ in three stocks. The first year, stock A paid $6\%$ dividends and increased $3\%$ in value; stock B paid $7\%$ dividends and increased $4\%$ in value; stock C paid $8\%$ dividends and increased $2\%$ in value. IF the total dividends were $$2730$ and the total increase in value was $$1080,$ how much was invested in each stock?