Question

Students and adults purchased tickets for a movie. Student tickets cost $8 each, and adult tickets cost $12 each. A total of $6,800 was collected from the sale of 640 tickets. Write a system of equations to find the number of student tickets, s, and the number of adult tickets, a, that were sold at the movie theater.

a) 8s + 12a = 6,800 and s + a = 640
b) 8s - 12a = 6,800 and s + a = 640
c) 12s + 8a = 6,800 and s + a = 640
d) 12s - 8a = 6,800 and s + a = 640

Answer 1

The correct system of equations to find the number of student and adult tickets sold at the movie theater is 8s + 12a = 6,800 (total revenue from sales) and s + a = 640 (total number of tickets sold).

Step-by-step explanation:

To find the number of student tickets, s, and the number of adult tickets, a, that were sold for a movie, we can use a system of equations based on the price per ticket and the total amount collected. The first equation comes from the total amount of money collected:

8s + 12a = 6,800

Student tickets cost $8 each, and adult tickets cost $12 each. The total collected from ticket sales was $6,800.

The second equation comes from the total number of tickets sold:

s + a = 640

This represents the total number of student and adult tickets, which adds up to 640.

With these two equations, we can solve for the variables s and a. The correct system of equations to represent this situation is choice a) from the question.