Loretta walked a distance of $\displaystyle{2}\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ miles to the library. When she was done there, she walked $\displaystyle{1}\frac{{1}}{{5}}\usepackage{cmbright}\Huge\$ miles to the supermarket. After that she took the bus home. What was the total distance that she walked?

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