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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.