.
Since the condition says nothing about the attendance, it is possible, by default, to assume that all 315 tickets were sold.
Actually, we do not need to know about the theater' capacity - we only need to know the number of the ticket sold.
With this assumption, see my solution below.
Let x be the number of adults.
Then the number of children is 2x, according to the condition, and
the students are the rest (315 - x - 2x) = 315 - 3x persons.
Now you can write the money equation (revenue equation)
5*(2x) + 7*(315-3x) + 12*x = 2294.
Simplify and solve for x
10x + 7*315 - 21x + 12x = 2294
x = 2294 - 7*315 = 89.
The problem is just solved.
ANSWER. 89 adults; 2*89 = 178 children, and the rest 315 - 89 - 178 = 48 are students.
CHECK. 89*12 + 178*5 + 48*7 = 2294 dollars. ! Precisely correct !
Solved.
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The lesson to learn from this solution:
For the first glance, 3 unknowns are required to solve the problem.
But, actually, it can be solved using only one unknown.