###### Example 5.4.6 Applications of Systems of Equations

The Rusk Ranch Nature Center^{ 1 } in south-western Oregon is a volunteer run nonprofit that exists to promote the wellbeing of the local communities and conserve local nature with an emphasis on native butterflies. They sell admission tickets: \(\$6\) for adults and \(\$4\) for children. Amanda, who was working at the front desk, counted that one day she sold a total of \(79\) tickets and had \(\$384\) in the register from those ticket sales. She didn't bother to count how many were adult tickets and how many were child tickets because she knew she could use math to figure it out at the end of the day. So, how many of the \(79\) tickets were adult and how many were child?