Question 78321
<pre>
Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the receipts were $2380, how many of each type of ticket were sold?


What is asked in the problem?
    How many of each type of tickets were sold?

Given:
Tickets for a play at the community theater cost $16 for an adult 
and $2 for a child. 
If 210 tickets were sold and the receipts were $2380.

Representation:
Let x be the number of tickets sold for adults
    y be the number of tickets sold for kids

Equations:
The tickets sold were 210. adult's tickets plus children's ticket
   x + y = 210

The receipt cost 2380. Adults' ticket cost $16 and children's $2.
  16x + 2y = 2380

Solve the system of equations

    x +  y = 210        
  16x + 2y = 2380
___________________


Multiply -2 to x + y = 210 to eliminate y then add the 2 equations

  -2x - 2y = -420        
  16x + 2y = 2380
___________________

   14x     = 1960     Divide both sides by 14
         x = 140      there are 140 adult tickets sold


Choose either of the 2 equation. Substitute the value of x to find y.

   x + y = 210
 140 + y = 210
       y = 210 - 140
       y = 70            There are 70 children tickets sold.


Checking

    x + y = 210 ; x = 140 & y = 70
 140 + 70 = 210 
      210 = 210    True


         16x + 2y = 2380
16 (140) + 2 (70) = 2380
       2240 + 140 = 2380
             2380 = 2380    True


Therefore the solution we have is correct x = 140 and y = 70. There are 140 adult tickets sold and 70 children tickets sold.


Rmromero