You have $$50,000$ and wish to invest part at $10\%$ and the rest at $6\%.$ How much should be invested at each rate to produce the same return as if it all had been invested at $9\%?$

A$.$ $$37,000$ at $6\%,$$$13,000$ at $10\%$

B$.$ $$37,500$ at $10\%,$$$12,500$ at $6\%$

C$.$ $$37,500$ at $6\%,$$$12,500$ at $10\%$

D$.$ $$37,000$ at $10\%,$$$13,000$ at $6\%$