Question

A movie theater sells tickets for $9.00 each, with seniors' tickets for $7.00. One evening the theater sold 600 tickets and took in $4,760 in revenue. How many seniors' tickets were sold?

A. 320
B. 280
C. 200
D. 400

Answer 1

After setting up and solving a system of equations based on the given information, it was determined that 320 seniors' tickets were sold during the evening in question.

Step-by-step explanation:

The question involves setting up and solving a system of linear equations, which is a common task in algebra. The system we'll set up uses two equations based on the information given in the question:

1. The total number of tickets sold (regular plus seniors' tickets) is 600.
2. The total revenue from ticket sales is $4,760.

We let x represent the number of regular tickets sold at $9.00 each, and y represent the number of seniors' tickets sold at $7.00 each. Thus, we can write the following equations:

• x + y = 600 (1)
• 9x + 7y = 4,760 (2)

Now we can solve this system by using the substitution or elimination method. For simplicity, we will use the elimination method. Multiply equation (1) by 7, the price of a seniors' ticket, and subtract it from equation (2):

• 7x + 7y = 4,200 (3)
• 9x + 7y = 4,760 (2)
• 2x = 560 (4)

Dividing equation (4) by 2, we find x = 280. This means 280 regular tickets were sold. Substituting x = 280 into equation (1), we get y = 600 - 280 = 320.

Therefore, 320 seniors' tickets were sold, which corresponds to option A.