A theater contains 460 seats and the ticket prices for a recent play were $52 for adults and $26 for children. If the total proceeds were $16,276 for a sold-out matinee, how many of each type of ticket were sold?

The answer to your question is There were sold 166 adult tickets and 294

                                                     children tickets.

Step-by-step explanation:

Data

Total number of seats = 460

cost for adults = a = $52

cost for children = c = $26

Total cost = $16276

Process

1.- Write equations to solve this problem

              a + c = 460                    Equation l

         52a + 26c = 16276             Equation ll

2.- Solve the system of equation by substitution.

-Solve equation l for a

             a = 460 - c

-Substitute a in equation ll

         52(460 - c) + 26c = 16276

-Expand

         23920 - 52c + 26c = 16276

-Simplify

                     -26c = 16276 - 23920

                     -26c = -7644

                          c= -7644/-26

                          c = 294

3.- Find a

                        a = 460 - 294

                        a = 166

166 adult tickets and 294 children tickets were sold.

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of children tickets that were sold.

The ticket prices for a recent play were $52 for adults and $26 for children. If the total proceeds were $16,276 for a sold-out matinee, it means that

52x + 26y = 16276- - - - - - - - - 1

The theater contains 460 seats. Since it was a sold-out matinee, it means that

x + y = 460

Substituting x = 460 - y into equation 1, it becomes

52(460 - y) + 26y = 16276

23920 - 52y + 26y = 16276

- 52y + 26y = 16276 - 23920

- 26y = - 7644

y = - 7644/- 26

y = 294

x = 460 - y = 460 - 294

x = 166