SOLUTION: At a Performing Arts Center, seats in the orchestra section cost $18 and seats in the balcony cost $12.If they were 120 seats sold for one performance, for a total revenue of $1920

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Question 1127300: At a Performing Arts Center, seats in the orchestra section cost $18 and seats in the balcony cost $12.If they were 120 seats sold for one performance, for a total revenue of $1920, how many balcony seats were sold?
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
O = number of orchestra seats sold
B = number of balcony seats sold

O + B = 120         (1)  (from the number of tickets sold info)
18O + 12B = 1920    (2)  (from the revenue info)

Will solve by substitution. (1) implies O = 120 - B. Substitute "120-B" for "O" in (2):
18(120-B) + 12B = 1920
2160 - 18B + 12B = 1920
-6B = 1920 - 2160
-6B = -240 —> B = 240/6 = 40
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Ans: 40 balcony seats were sold
—
Check: 40 balcony seats —> 80 orchestra seats (using (eq 1))
40*12 + 80*18 = 480 + 1440 = 1920 (revenue info checks out)



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