One night a theater sold 548 movie tickets an adult's tickets cost 6.50 and a child's ticket cost 3.50

For the answer to the question above, let's say there were x child tickets and y adults tickets. 

The total amount sold is: x + y = 548 

The total cost of child's tickets: 3.50 * x 
The total cost of adults tickets: 6.50* y 

Now the cost of ALL tickets sold is 2881: 3.5*x + 6.5*y = 2881 

These are equations you want to solve: 
x + y = 548 
3.5*x + 6.5*y = 2881