SOLUTION: 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 mon

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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?
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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?
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Let A = # of adults tickets, S = # of students tickets.

Then the number of children tickets is A + S - 200.

You have these equations

  A +   S +    (A+S-200) =   400,    (1)
40A + 20S + 10*(A+S-200) = 10600.    (2)


Simplify and write in the standard form

 2A +  2S =   600,                  (1')
50A + 30S = 12600.                  (2')


Or even simpler

  A + S   = 300,                    (1'')
5A + 3S   = 1260                    (2'')


From (1''), express A = 300-S and substitute it into (2''). You will get

5*(300-S) + 3S = 1260.


From this point, please complete the solution on your own.