I need help with this problem
tickets $7 in advance, $9 at the door. 684 tickets were sold with a total $5740. how many tickets were sold at the door?
In these types of problems, you will get two equations: the first equation relates to the dollars and the second equation relates to "how many".
OK, lets call advance tickets = a and door tickets = d. These are our unknowns.
The first equation is about the money. $7a+$9d=$5740.
The second equation is about how many. a+d=684.
We have 2 equations and 2 unknowns, so we can use substitution method to solve this thing! Let's rewrite the second equation a=684-d (you could also solve this by writing d=684-a, you choose).
Substituting our new second equation into our first equation, we get
$7(684-d)+$9d=$5740. Now using your skills to solve equations, here are the steps:
Mental Math approach:
Assuming all the tickets were sold in advance, then 684 tickets would have been sold with 7*684 = $4788
Since the actual ticket revenue was $5740, the difference 5740 - 4788 = $952 would be the "extra" revenue.
Therefore, the actual number of tickets sold at the door was 952/2 = 476 tickets.