Question

Students and adults purchased tickets for a movie. All tickets were sold at the ticket booth. Student tickets cost $8 each, and adult tickets cost $12 each. A total of $6,800 was collected. 640 tickets were sold.

A) 400 student tickets and 240 adult tickets
B) 320 student tickets and 320 adult tickets
C) 240 student tickets and 400 adult tickets
D) 280 student tickets and 360 adult tickets

Answer 1

The problem can be solved by setting up a system of equations and using either substitution or elimination method. The number of student tickets sold is 220 and the number of adult tickets sold is 420.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the information given. Let's assume the number of student tickets sold is S and the number of adult tickets sold is A.

From the problem, we know that:

1. S + A = 640 (equation 1)
2. 8S + 12A = 6800 (equation 2)

We can solve this system of equations by substitution or elimination. Let's use the substitution method.

1. In equation 1, solve for S:
   S = 640 - A
2. Substitute this value of S in equation 2:
   8(640 - A) + 12A = 6800
3. Simplify the equation:
   5120 - 8A + 12A = 6800
4. Combine like terms:
   4A = 1680
5. Divide both sides by 4:
   A = 420
6. Substitute this value of A in equation 1 to find S:
   S + 420 = 640
7. Solve for S:
   S = 220

Therefore, the number of student tickets sold is 220 and the number of adult tickets sold is 420.

So, the answer is A) 400 student tickets and 240 adult tickets.