SOLUTION: Problem Page Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $20 . For one performance, there were 3

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Problem Page Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $20 . For one performance, there were 3      Log On


   

Question 1111570: Problem Page Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $20 . For one performance, there were 35 tickets sold in all, and the total amount paid for them was $800 . How many tickets of each type were sold?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x same-day
y advanced
system%2820x%2B25y=800%2Cx%2By=35%29

4x%2B5y=160
-
4%2835-y%29%2B5y=160


system%28x=15%2Cy=20%29
15 of same-day tickets
20 of advanced tickets

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a quick path to the solution using mental arithmetic and some logical reasoning.

(1) If all 35 tickets had been same day tickets, the total amount paid would have been $700, which is $100 less than the actual total.
(2) Each advance ticket costs $5 more than each same day ticket.
(3) To make the other $100 of the actual total, the number of advance tickets has to be 100/5 = 20.

So there were 20 advance tickets, which means there were 35-20=15 same day tickets.