Question

A theatre contains 487 seats and the ticket prices for a recent play were $47 for adults and $29 for children. If the total proceeds were $17,525 for a sold-out matinee, how many of each type of ticket were sold?

Answer 1

Explanation:

Let's use A to represent the number of adult tickets sold and C to represent the number of children tickets sold. We can set up two equations based on the information given:

The total number of tickets sold is the sum of adult and children tickets:

A + C = 487

The total proceeds from ticket sales is the product of the number of tickets and their respective prices:

47A + 29C = 17525

We can use the first equation to solve for one of the variables in terms of the other:

C = 487 - A

Substituting this expression for C into the second equation, we get:

47A + 29(487 - A) = 17525

Simplifying and solving for A:

18A + 14123 = 17525

18A = 3402

A = 189

So 189 adult tickets were sold. Using the equation C = 487 - A, we can find the number of children tickets sold:

C = 487 - 189 = 298

Therefore, 189 adult tickets and 298 children tickets were sold for the matinee.