Question 344448
A theater sold 480 tickets for a play last night. Floor seats sold for $30.00 each and balcony seats sold for $24.00 each. The total amount collected for the 480 tickets was $13,200.00. How many seats of each type were sold? 
.
You could solve it your way:
Let f = number of floor tix
and b = number of balcony tix
.
Then, from: "A theater sold 480 tickets" we get:
f + b = 480 (equation 1)
.
From: "Floor seats sold for $30.00 each and balcony seats sold for $24.00 each. The total amount collected for the 480 tickets was $13,200.00" we get:
30f + 24b = 13200 (equatio 2)
.
Now, we can either apply the "substitution" or "addition" method.  I'll apply the addition method, starting with our two equations:
f + b = 480
30f + 24b = 13200
.
Multiply the top equation by -24:
-24f - 24b = -11520
30f + 24b = 13200
.
Add both equations together:
-24f - 24b = -11520
30f + 24b = 13200
-----------------------
6f = 1580
f = 280 tickets (floor)
.
Substitute the above back into equation 1 to find b:
f + b = 480
280 + b = 480
b = 200 tickets (balcony)