document.write( "Question 73828: A total of 434 people attended a community theatre performance. The admission prices were $9.00 for adults, $7.50 for students, and $8.00 for senior citizens. The ticket sales totaled $3712. At the theatre's next board meeting, the finance manager proposed that for the next play they raise prices to $11.00 for adults, $8.50 for students, and $8.50 for senior citizens. He said that if the exact same number of people attend the next performance, the ticket sales would be $4374. How many adults, students, and senior citizens attended the play? \n" ); document.write( "
Algebra.Com's Answer #52867 by Edwin McCravy(20056)\"\" \"About 
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A total of 434 people attended a community theatre performance. The admission prices were $9.00 for adults, $7.50 for students, and $8.00 for senior citizens. The ticket sales totaled $3712. At the theatre's next board meeting, the finance manager proposed that for the next play they raise prices to $11.00 for adults, $8.50 for students, and $8.50 for senior citizens. He said that if the exact same number of people attend the next performance, the ticket sales would be $4374. How many adults, students, and senior citizens attended the play?
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document.write( "Let A = number of Adults who attended\r\n" );
document.write( "Let S = number of Students who attended\r\n" );
document.write( "Let C = number of senior Citizens who \r\n" );
document.write( "attended\r\n" );
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document.write( "A total of 434 people attended a community \r\n" );
document.write( "theatre performance.\r\n" );
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document.write( "A + S + C = 434\r\n" );
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document.write( "The admission prices were $9.00 for \r\n" );
document.write( "adults, $7.50 for students, and $8.00 for \r\n" );
document.write( "senior citizens. The ticket sales totaled \r\n" );
document.write( "$3712. \r\n" );
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document.write( "9A + 7.5S + 8C = 3712\r\n" );
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document.write( "At the theatre's next board meeting, the \r\n" );
document.write( "finance manager proposed that for the next \r\n" );
document.write( "play they raise prices to $11.00 for adults, \r\n" );
document.write( "$8.50 for students, and $8.50 for senior \r\n" );
document.write( "citizens. He said that if the exact same \r\n" );
document.write( "number of people attend the next performance, \r\n" );
document.write( "the ticket sales would be $4374. \r\n" );
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document.write( "11A + 8.5S + 8.5C = 4374\r\n" );
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document.write( "So we have this system of three \r\n" );
document.write( "equations in three unknowns.\r\n" );
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document.write( "  A +    S +    C =  434\r\n" );
document.write( " 9A + 7.5S +   8C = 3712\r\n" );
document.write( "11A + 8.5S + 8.5C = 4374\r\n" );
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document.write( "You can simplify the 2nd and 3rd \r\n" );
document.write( "equations:\r\n" );
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document.write( "Simplifying the 2nd equation:\r\n" );
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document.write( "   9A + 7.5S + 8C = 3712\r\n" );
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document.write( "First clear of decimals by multiplying \r\n" );
document.write( "through by 10\r\n" );
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document.write( "  90A + 75S + 80C = 37120\r\n" );
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document.write( "Now divide every term through by 5\r\n" );
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document.write( "   18A + 15S + 16C = 7424\r\n" );
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document.write( "Simplifying the 3rd equation:\r\n" );
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document.write( "11A + 8.5S + 8.5C = 4374\r\n" );
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document.write( "First clear of decimals by multiplying \r\n" );
document.write( "through by 10\r\n" );
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document.write( "110A + 85S + 85C = 43740\r\n" );
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document.write( "Now divide every term through by 5\r\n" );
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document.write( "22A + 17S + 17C = 8748\r\n" );
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document.write( "Now the system is\r\n" );
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document.write( "  A +   S +   C =  434\r\n" );
document.write( "18A + 15S + 16C = 7424\r\n" );
document.write( "22A + 17S + 17C = 8748\r\n" );
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document.write( "That's a little easier to solve.\r\n" );
document.write( "Can you solve it? If not post\r\n" );
document.write( "again asking how to.\r\n" );
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document.write( "Answer:\r\n" );
document.write( "A = 274 S = 68, C = 92,\r\n" );
document.write( "that is, 274 adults, 68 students, \r\n" );
document.write( "and 92 senior citizens attended \r\n" );
document.write( "the play.\r\n" );
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document.write( "Edwin
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