Question 1176309
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We assume that all 291 tickets are sold.



<pre>
Let "a" be the number of adults;  then the number of children is  (2a).


The number of students is the rest, (291-a-2a) = 291-3a.


The "money" equation is


    12a + 5*(2a) + 7*(291-3a) = 2116  dollars.


Simplify and solve for "a".


    12a + 10a + 7*207 - 21a = 2116 - 7*291,

    a = 79.


<U>ANSWER</U>.  79 adults;  2*79 = 158 children  and  (291-3*79) = 54 students.


<U>CHECK</U>.  79*12 + 5*158 + 54*7 = 2116  dollars, total revenue.   ! Correct !
</pre>

Solved.


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This problem is to be solved using one equation in one unknown.


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