SOLUTION: 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 sol

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