A woman has $$49,000$ to invest. She has decided to invest all of it by purchasing some shares of stock in each of three companies$$a fast$-$food chain that sells for $$20$ per share and has an expected growth of $11\mathrm{.}5\%$ per year, a software company that sells for $$20$ per share and has an expected growth of $15\%$ per year, and a pharmaceutical company that sells for $$70$ per share and has an expected growth of $10\%$ per year. She plans to buy twice as many shares of stock in the fast$-$food chain as in the pharmaceutical company. If her goal is $12\%$ growth per year, how many shares of each stock should she buy?

fast$-$food chain

software company

pharmaceutical company