Question

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.

Answer 1

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. 

Answer 2

$30x+$12y=$19080
x+y=960
y=960-x
30*x+12*960-x=$19080
30x-12x=-7560
-18x=-7560
x=-7560/-18
x=420
therefore there are 420 children
960-420=540
and there are 540 adults