If Jessie has n nickels, d dimes, and q quarters, then:

$\displaystyle{n}+{d}+{q}={30}\usepackage{cmbright}\Huge\$

$\displaystyle{0.05}{n}+{0.10}{d}+{0.25}{q}={3.45}\usepackage{cmbright}\Huge\$

$\displaystyle{n}={q}+{5}\usepackage{cmbright}\Huge\$ or $\displaystyle{n}-{q}={5}\usepackage{cmbright}\Huge\$

Multiply the second equation by 100: $\displaystyle{5}{n}+{10}{d}+{25}{q}={345}\usepackage{cmbright}\Huge\$

Multiply the first equation by $\displaystyle-{10}\usepackage{cmbright}\Huge\$ and add to the above: $\displaystyle-{5}{n}+{15}{q}={45}\usepackage{cmbright}\Huge\$

Multiply the third by $\displaystyle{5}\usepackage{cmbright}\Huge\$ and add to this: $\displaystyle{10}{q}={70}\usepackage{cmbright}\Huge\$ or $\displaystyle{q}={7}\usepackage{cmbright}\Huge\$

From the third equation: $\displaystyle{n}={12}\usepackage{cmbright}\Huge\$ , and from the first equation: $\displaystyle{d}={11}\usepackage{cmbright}\Huge\$