Question

Tickets at the movie theater are $9.00 for adults. Seniors receive a discount and only have to pay $6.00. The capacity of the theater is 80 people. If the theater was at full capacity and made $675, then __?__ seniors bought tickets for the movie.

A) 15
B) 30
C) 45
D) 60
E) 75

Answer 1

To solve the problem, we set up a system of equations based on the capacity of the theater, the price of tickets, and the total revenue. By substituting the value of adults in terms of seniors into the revenue equation, we can solve for the number of seniors and find that 15 seniors bought tickets.

Step-by-step explanation:

To determine how many seniors bought tickets for the movie, we need to set up an equation based on the total revenue and the price of tickets for adults and seniors. Let's denote the number of seniors as 'S' and the number of adults as 'A'.

Since we know the total capacity is 80 people, we have:

A + S = 80 (Total number of people)

We also know that the total revenue is $675, and the price for adults is $9, and for seniors, it is $6. So:

9A + 6S = 675 (Total revenue from ticket sales)

Solving the System of Equations

Using the equation A + S = 80, we can express A in terms of S: A = 80 - S.

Substituting this into the revenue equation:

9(80 - S) + 6S = 675

Simplifying:

720 - 9S + 6S = 675

720 - 3S = 675

-3S = 675 - 720

-3S = -45

S = 15

Therefore, the number of seniors who bought tickets for the movie is 15.