document.write( "Question 1074578: A concert audience of 400 people consists of adults, students, and children. The ticket prices are $40 for adults, $20 for students, and $10 for children. The total amount of money taken in was $10,600. The numbers of children tickets sold is 200 less than the number of adults and student tickets in total. How many adults, students, and children are in attendance? \n" ); document.write( "

Algebra.Com's Answer #689226 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "A concert audience of 400 people consists of adults, students, and children. The ticket prices are $40 for adults, $20 for students,
\n" ); document.write( "and $10 for children. The total amount of money taken in was $10,600. The numbers of children tickets sold is 200 less
\n" ); document.write( "than the number of adults and student tickets in total. How many adults, students, and children are in attendance?
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document.write( "Let A = # of adults tickets, S = # of students tickets.\r\n" );
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document.write( "Then the number of children tickets is A + S - 200.\r\n" );
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document.write( "You have these equations\r\n" );
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document.write( "  A +   S +    (A+S-200) =   400,    (1)\r\n" );
document.write( "40A + 20S + 10*(A+S-200) = 10600.    (2)\r\n" );
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document.write( "Simplify and write in the standard form\r\n" );
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document.write( " 2A +  2S =   600,                  (1')\r\n" );
document.write( "50A + 30S = 12600.                  (2')\r\n" );
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document.write( "Or even simpler\r\n" );
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document.write( "  A + S   = 300,                    (1'')\r\n" );
document.write( "5A + 3S   = 1260                    (2'')\r\n" );
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document.write( "From (1''), express A = 300-S and substitute it into (2''). You will get\r\n" );
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document.write( "5*(300-S) + 3S = 1260.\r\n" );
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document.write( "From this point, please complete the solution on your own.\r\n" );
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