Let $\displaystyle{p}=\usepackage{cmbright}\Huge\$ the cost of one ounce of peanuts and $\displaystyle{c}=\usepackage{cmbright}\Huge\$ the cost of one ounce of cashews. Then the information leads you to two equations:

$\displaystyle{15}{p}+{5}{c}={4.75}\usepackage{cmbright}\Huge\$ and $\displaystyle{5}{p}+{15}{c}={6.25}\usepackage{cmbright}\Huge\$

Multiply the first equation by $\displaystyle-{3}\usepackage{cmbright}\Huge\$ : $\displaystyle-{45}{p}-{15}{c}=-{14.25}\usepackage{cmbright}\Huge\$

Add this to the second equation: $\displaystyle-{40}{p}=-{8}\usepackage{cmbright}\Huge\$ , so $\displaystyle{p}={0.20}\usepackage{cmbright}\Huge\$

Substitute into the first equation: $\displaystyle{15}{\left({0.20}\right)}+{5}{c}={4.75}\usepackage{cmbright}\Huge\$ or $\displaystyle{3.00}+{5}{c}={4.75}\usepackage{cmbright}\Huge\$

This gives you $\displaystyle{5}{c}={1.75}\usepackage{cmbright}\Huge\$ , so $\displaystyle{c}={0.35}\usepackage{cmbright}\Huge\$ .