Question 1175370
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A movie theater has a seating capacity of 361. The theater charges $5.00 for children, 
$7.00 for students, and $12.00 of adults. There are half as many adults as there are children. 
If the total ticket sales was $ 2614, How many children, students, and adults attended?
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<pre>
x adults

2x children

and (361 - x - 2x) = (361-3x) students (the rest . . . )



Total money equation

    12x + 5*(2x) + 7*(361-3x) = 2614   dollars


Simplify and solve

    12x + 10x - 21x = 2614 - 7*361

           x        =     87


<U>ANSWER</U>.  87 adults;  2*87 = 174 children  and the rest  361-87 - 174 = 100 are students.


<U>CHECK</U>.   87*12 + 5*174 + 7*100 = 2614 dollars, in total.    ! Correct !
</pre>

Solved.


Notice that I solved the problem using only one equation and only one single unknown.


It is how this problem SHOULD be solved (!)



Also, notice that the capacity of the theater is IRRELEVANT to this problem.


We only should know (instead of the total capacity) the total number of SOLD TICKETS.