A $$36,000$ portfolio is invested in a risk$-$free security and two stocks. The beta of stock A is $1\mathrm{.}29$ while the beta of stock B is $0\mathrm{.}90.$ One$-$half of the portfolio is invested in the risk$-$free security. How much is invested in stock A if the beta of the portfolio is $0\mathrm{.}55$