Question

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 $50. For one performance, $30 advance tickets and $35 same-day tickets were sold. The total amount paid for the tickets was $1575. What was the price of each kind of ticket?

Answer 1

A + S = 50 (Combined cost of one advance and one same-day ticket is $50).
30A + 35S = 1575 (Total amount paid for the tickets was $1575).
Now we can solve this system of equations to find the prices of each kind of ticket. Let's do the math:

From the first equation, we can express S in terms of A: S = 50 - A.

Substitute this value of S into the second equation:

30A + 35(50 - A) = 1575
30A + 1750 - 35A = 1575
-5A = 1575 - 1750
-5A = -175
A = 35

Now that we have the value of A (the price of one advance ticket), we can find the price of one same-day ticket (S):

S = 50 - A = 50 - 35 = 15

So, the price of each kind of ticket is $35 for advance tickets and $15 for same-day tickets