[tex]h-the\ handbag\\s-shoes\\\\ \left\{\begin{array}{ccc}h+3s=324\\h=\frac{1}{2}\cdot3s\end{array}\right\\\left\{\begin{array}{ccc}h+3s=324\\h=\frac{3}{2}s&/\cdot\frac{2}{3}\end{array}\right\\\left\{\begin{array}{ccc}h+3s=324\\s=\frac{2}{3}h\end{array}\right\\\\substitute:\\\\h+3\cdot\frac{2}{3}h=324\\h+2h=324\\3h=324\ \ \ \ /:3\\h=108\\\\Answer:Cost\ of\ the\ handbag\ is\ \$108.[/tex]