If she has p pennies, n nickels, and d dimes, then:

$\displaystyle{p}+{n}+{d}={16}\usepackage{cmbright}\Huge\$

$\displaystyle{0.01}{p}+{0.05}{n}+{0.10}{d}={1.22}\usepackage{cmbright}\Huge\$

$\displaystyle{2}{p}={n}\usepackage{cmbright}\Huge\$ or $\displaystyle{2}{p}-{n}={0}\usepackage{cmbright}\Huge\$

Multiply the second equation by 100: $\displaystyle{p}+{5}{n}+{10}{d}={122}\usepackage{cmbright}\Huge\$

Multiply the first equation by $\displaystyle-{10}\usepackage{cmbright}\Huge\$ and add to the above: $\displaystyle-{9}{p}-{5}{n}=-{38}\usepackage{cmbright}\Huge\$

Multiply the third by $\displaystyle-{5}\usepackage{cmbright}\Huge\$ and add to this: $\displaystyle-{19}{p}=-{38}\usepackage{cmbright}\Huge\$ or $\displaystyle{p}={2}\usepackage{cmbright}\Huge\$

From the third equation $\displaystyle{n}={4}\usepackage{cmbright}\Huge\$ , and from the first equation $\displaystyle{d}={10}\usepackage{cmbright}\Huge\$ .