Question 1203711
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A movie theater has a seating capacity of 367. 
The theater charges $5.00 for children, $7.00 for students, and the $12.00 for adults. 
There are half as many adults as there are children if the total tickets sales was $2668, 
how many children, students, and adults attended?
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        It may seem amazing, but the problem can be solved using only one unknown 

        and one equation. I will show this solution method below.

        Surely, the theater is considered to be fully filled, as it is usually 

        assumed in such problems,  by default and from context.



<pre>
Let x be the number of adults.
Then the number of children is 2x, from the problem,
and the number of students is (367-x-2x) = (367-3x).


Write the total money equation

    5*(2x) + 7*(367-3x) + 12x = 2668  dollars.


Simplify this equation and find x

    10x + 7*367 - 21x + 12x = 2668

    10x         - 21x + 12x = 2668 - 7*367

            x               =     99.


<U>ANSWER</U>.  99 adults;  2*99 = 198 children,  and  367-99-198 = 70 students.


<U>CHECK</U> the total money: 99*12 + 198*5 + 70*7 = 2668  doll;ars.    ! correct !
</pre>

Solved.


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<H3>The lesson to learn:</H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem seem to be solved using three &nbsp;(or two) &nbsp;unknown;

    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;but in reality, &nbsp;it can be solved using one unknown and one equation,

    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;saving your time and diminishing the number of erros.


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Your task is to learn to recognize such problems from the first glance.