SOLUTION: Problem Page 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 $45 . For one performan

Question 1110761: Problem Page 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 $45 . For one performance, 40 advance tickets and 20 same-day tickets were sold. The total amount paid for the tickets was $1300 . What was the price of each kind of ticket?
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Combine the tickets in groups in this way:


 40 advance tickets + 20 same day tickets = 

(20 advance tickets + 20 same say tickets) + 20 advance tickets.


Now the total cost is


1300 = 20*45 + 20a,  where "a" is the cost of the advance ticket.


It gives  20a = 1300-900 = 400.


Hence,  a =  = 20 dollars is the price of one advance ticket.


Then the price of one same day ticket is  45-20 = 25 dollars.

Solved.

The lesson to learn from this solution: You do not need to solve the system of equations to get the answer.

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