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?
+539 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.
Check
38*15=570
82*10=820
820+570=1390
+34 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
\(10y+15x=1390\)
\(y+x=120\)
We can solve elimination (Feel free to use a different strategy):
Multiply the bottom equation by \(10\)
\(10y+10x=1200\)
Subtract the bottom equation
\(5x=190\)
Divide both sides by \(5\)
\(x=38\)
Plug that value into the bottom equation (or the top if you want)
\(y+38=120\)
Subtract \(38\) from both sides
\(y=82\)
\(82\) tickets were bought at the door.
Hope this helped!!!
-Ako
