A College sold Advance tickets to a play at $4 per ticket. Anyone who attended and purchased a ticket at the door had to pay $5 a ticket. A total of 480 people attended the play, and the revenue (earnings) from the ticket sales was$ 2100. How many people bought tickets at the door?
ap + door=480
4*ap + 5*door=2100
in the first equation, ap= 480-door
Put that into the second equation for ap, and then solve.
Let x =the number of people who paid at the door
4(480-x)+5x=2100 Distribute
1920-4x+5x=2100 add like terms
1920-9x=2100
-1920-9x=2100-1920
-9x=180 Divide by nine
x=-20 pe0ple at the door
To solve the system of equations, substitute the value of ap from the first equation into the second equation:
4*(480 - door) + 5*door = 2100
Now, distribute the 4 to the terms inside the parentheses:
1920 - 4*door + 5*door = 2100
Combine like terms:
1920 + door = 2100
Isolate the variable by subtracting 1920 from both sides:
door = 2100 - 1920
door = 180
The number of people who bought tickets at the door is 180.