SOLUTION: Tickets sold in advance for a play cost $3 each. Tickets sold at the door for the same play cost $5 each. If 100 tickets were sold for this play for a total of $460, how many were

Question 622170: Tickets sold in advance for a play cost $3 each. Tickets sold at the door for the same play cost $5 each. If 100 tickets were sold for this play for a total of $460, how many were purchased at the door?
Answer by matineesuxxx(27) (Show Source): You can put this solution on YOUR website!
Let x represent tickets sold at the door
Let y represent tickets sold in advance
therefore,
5x + 3y = 460 ( this is the statement for total amount of money)
x + y = 100 ( this is the statement for number of tickets sold)
now use either equation to solve for y, it just happens that x + y = 100 is the easiest to do this with,
this gives use the answer,
y = 100 - x
now plug this into our money equation and you get,
5x + 3(100-x) = 460
now simplify,
5x + 300 - 3x = 460
2x = 160
x = 80
Therefore, 80 tickets were sold at the door.
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