At a charity banquet, tickets cost $10 for one adult and $5 for one child. The charity collects $2,750. The number of tickets sold to adults, a, is 50 more than the number of tickets sold to children, c. This can be described by a system of equations and by a graph:

$\displaystyle{10}{a}+{5}{c}={2},{750}\usepackage{cmbright}\Huge\$ and $\displaystyle{a}={c}+{50}\usepackage{cmbright}\Huge\$

How many adult tickets were sold?