A retired couple have $$300,000$ to invest and want to earn $$30,000$ per year in interest. The safer investment yields $9\mathrm{.}5\%,$ but they can supplement their earnings by investing some of their money at $11\%.$ How much should they invest at each rate to earn $$30,000$ per year?

They should invest at $9\mathrm{.}5\%$ and at $11\%.$