Question

A group of people sells tickets for a game. Tickets for lower-level seats sell for $35 each, and tickets for upper-level seats sell for $25 each. The stage sells 350 for $10,250. So, how many tickets of each were sold?

A) 100 lower-level tickets and 250 upper-level tickets
B) 150 lower-level tickets and 200 upper-level tickets
C) 200 lower-level tickets and 150 upper-level tickets
D) 250 lower-level tickets and 100 upper-level tickets

Answer 1

By setting up a system of linear equations based on the number of tickets and total sales, we calculate that 150 lower-level tickets and 200 upper-level tickets were sold.

Step-by-step explanation:

To solve this problem, we need to set up a system of linear equations using the information provided about the ticket prices and total sales.

Let's let L represent the number of lower-level tickets sold and U represent the number of upper-level tickets sold. We can create two equations based on the following conditions:

1. The total number of tickets sold is 350: L + U = 350
2. The total revenue from selling the tickets is $10,250: 35L + 25U = 10,250

To solve the system, we can use substitution or elimination. We'll utilize the elimination method:

1. Multiply equation (1) by 25: 25L + 25U = 8,750
2. Subtract this new equation from equation (2): (35L + 25U) - (25L + 25U) = 10,250 - 8,750
3. Solve for L: 10L = 1,500, so L = 150
4. Substitute L = 150 into equation (1): 150 + U = 350, so U = 200

Therefore, 150 lower-level tickets and 200 upper-level tickets were sold. The correct answer is B) 150 lower-level tickets and 200 upper-level tickets.