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

$\displaystyle{p}+{n}+{d}={18}\usepackage{cmbright}\Huge\$

$\displaystyle{0.01}{p}+{0.05}{n}+{0.10}{d}={1.08}\usepackage{cmbright}\Huge\$

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

Multiply the second equation by 100: $\displaystyle{p}+{5}{n}+{10}{d}={108}\usepackage{cmbright}\Huge\$

Multiply the first equation by $\displaystyle-{5}\usepackage{cmbright}\Huge\$ and add to the above: $\displaystyle-{4}{p}+{5}{d}={18}\usepackage{cmbright}\Huge\$

Multiply the third equation by 2 and add to this: $\displaystyle{3}{d}={18}\usepackage{cmbright}\Huge\$ or $\displaystyle{d}={6}\usepackage{cmbright}\Huge\$

From the third equation $\displaystyle{p}={3}\usepackage{cmbright}\Huge\$ , and from the first equation $\displaystyle{n}={9}\usepackage{cmbright}\Huge\$ .