A bread recipe calls for $\displaystyle{2}\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ cups of whole-wheat flour, $\displaystyle\frac{{2}}{{3}}\usepackage{cmbright}\Huge\$ cup of rye flour, and $\displaystyle{2}\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ cups of white flour. How many total cups of flour are needed? Write your answer as a simplified mixed number.