Word problem

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 $45. For one performance, 25 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was $1375. What was the price of each kind of ticket?.

Answer 1

For this problem you're going to set up two equations, one showing the cost of the two tickets combined and another showing the profit from the sales of on performance. Let x be advanced tickets and y be same day tickets

 

x+y=45

25x+35y=1375

 

Now solve for one variable in one of the variables and plug it into the other equation. It's easiest to work with the first equation. 

 

Y=45-x

 

25x+35(45-x)=1375

25x+1575-35x=1375

1575-10x=1375

200=10x

x=20

 

so now we know an advanced ticket costs $20. After plugging that into the first equation we know that same day tickets cost $25.