A chef was preparing meatballs. He used a combination of $\displaystyle{4}\frac{{1}}{{3}}\usepackage{cmbright}\Huge\$ pounds of ground beef, $\displaystyle{2}\frac{{5}}{{6}}\usepackage{cmbright}\Huge\$ pounds of ground pork, and $\displaystyle{1}\frac{{1}}{{12}}\usepackage{cmbright}\Huge\$ pounds of ground veal. What was the total amount of ground meat in the mixture?

The answer should be written as a proper mixed number and should be simplified, if possible.