Tickets to a show cost $10 in advance and $15 at the door. If 120 tickets are sold for a total of $1390, how many tickets were bought in advance?
Here is how I solve it:
Say all the tix were bought in advance: that would mean 1200 dollars were sold. For each ticket we turn into bought at the door, we gain 5 dollars. The difference of 1390 and 1200 is 190. So 190/5 38 were bought at the door. So 82 were bought in advance.
We can solve this using a system of equations.
Let \(x=\)tickets bought at the door
Let \(y=\)tickets bought in advance
Our equations are
We can solve elimination (Feel free to use a different strategy):
Multiply the bottom equation by \(10\)
Subtract the bottom equation
Divide both sides by \(5\)
Plug that value into the bottom equation (or the top if you want)
Subtract \(38\) from both sides
\(82\) tickets were bought at the door.
Hope this helped!!!