Tickets to a musical cost $30 for adults and $12 for children. at one particular performance 960 people attended and $19 080 was collected in ticket sales. find the number of adults and the number of children who attended the performance.

In order to solve this, you have to set up a systems of linear equations.

Let's say that children = c and adults = a

30a + 12c = 19,080
a + c = 960

I'm going to show you how to solve this system of linear equations by substitution, the easiest way to solve in my opinion.

   a + c = 960 
       - c    -    c
  ⇒ Step 1: Solve for either a or c in either equation.
   a = 960 - c 

20(960 - c)+ 12c = 19,080
19,200 - 20c + 12c = 19,080
   19,200 - 8c = 19,080
 - 19,200         - 19,200
 ⇒ Step 2: Substitute in the value you got for a or c
         8c = -120                    into the opposite equation.                                                
         
          8         8
 
         c = -15

30a + 12(-15) = 19,080
   30a - 180 = 19,080
          + 180  +     180
 
   30a = 19,260
   
    30          30
     
       a = 642


I just realized that there can't be a negative amount of children, so I'm sorry if these results are all wrong.