document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #743678 by math_helper(2461) $\"\"$ $\"About$

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