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?
The book solves it by using the equation 30f+24(480-f)=13,200
f=number of floor tix
30f=total cost of floor tix
24(480-f)=total cost of balcony tix
Im not comprehending this way of solving, I remember in algebra class my professor using two different variables for each piece of the problem (floor tix=f) balcony tix=b) then using i think the distributive property?? Could you think of another way to help me understand?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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?
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You could solve it your way:
Let f = number of floor tix
and b = number of balcony tix
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Then, from: "A theater sold 480 tickets" we get:
f + b = 480 (equation 1)
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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)
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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
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Multiply the top equation by -24:
-24f - 24b = -11520
30f + 24b = 13200
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Add both equations together:
-24f - 24b = -11520
30f + 24b = 13200
-----------------------
6f = 1580
f = 280 tickets (floor)
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Substitute the above back into equation 1 to find b:
f + b = 480
280 + b = 480
b = 200 tickets (balcony)
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