Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $55. For one performance, 30 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was 1725. What was the price of each kind of ticket?
Let x be the price of an advance ticket and y be the price of a same-day ticket.
From the given information, we can create the following system of equations:
x + y = 55 (1)
30x + 35y = 1725 (2)
Now, we can solve this system of equations.
Multiplying equation (1) by 30, we get:
30x + 30y = 1650
Subtracting this equation from equation (2), we get:
5y = 75
y = 15
Now, substitute y = 15 back into equation (1):
x + 15 = 55
x = 40
Therefore, the price of an advance ticket is $40 and the price of a same-day ticket is $15.