Answer:
<h2>(170;120;60).</h2>
Step-by-step explanation:
<h3>We know that:</h3>
Capacity of the theater: 350 people.
Adults is half the students.
Children's cost: $4.50
Student's cost: $7.50
Adults' cost: $12.50
Total Sales: $2415
We are gonna call <em>x </em>the children, <em>y </em>the students and <em>z </em>the adults:
So, the equation to express the capacity of the theater would be:

But,
(adults are have students)
So, the expression would be: 
<h3>Solving <em>y's </em>and Isolating <em>x </em>: </h3>

<h3>Now, we need a expression for costs. We have:</h3>

<h3>Replacing the <em>x </em>and <em>z </em>equation:</h3>

<h3>Now, we solve for <em>y</em>:</h3>

<h3>But, we know that adults are half as many students, so:</h3>

<h3>Lastly,</h3>

<em>Therefore, there are 170 children, 120 students and 60 adults. Expressing the results as an ordered triple would be (170;120;60)</em>