Question

The community college fine arts department sold three types of tickets for its latest dance presentation: adult tickets at $20 each, student tickets at $12 each, and child tickets at $10 each. In total, 350 tickets were sold, generating $4,650 in revenue for the department in one night. The number of child tickets sold is the same as the number of adult tickets sold. Determine the number of each type of ticket sold by the department.

Provide answer below in the following format:
a. Adult tickets: __________
b. Student tickets: __________
c. Child tickets: __________

Answer 1

The number of adult tickets sold by the department is 155, while the number of student tickets sold is 0 and the number of child tickets sold is 155.

Step-by-step explanation:

To solve this problem, let's assign variables to the unknown quantities. Let x represent the number of adult tickets and c represent the number of child tickets sold. Since the number of child tickets sold is the same as the number of adult tickets sold, we can say c = x.

We know that the total number of tickets sold is 350. So, we have the equation x + x + c = 350. Simplifying this equation, we get 2x + c = 350.

The revenue generated from adult tickets is $20 times the number of adult tickets sold, which is 20x. Similarly, the revenue generated from child tickets is $10 times the number of child tickets sold, which is 10c. We are also given that the total revenue generated is $4,650. So, we have the equation 20x + 10c = 4650.

Substituting c = x into the second equation, we get 20x + 10(x) = 4650. Simplifying this equation, we get 30x = 4650. Dividing both sides by 30, we find x = 155.

Since c = x, the number of child tickets sold is also 155.

Therefore, the number of each type of ticket sold by the department is:

1. Adult tickets: 155
2. Student tickets: 0
3. Child tickets: 155