Question 1003069
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A movie theater charges $9.50 for an adult and $7.75 for a child to see a movie. 
If 92 people were at the 9:20 pm show and the total admission paid was $837.25, 
how many adult tickets were at the movies?
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        In this problem, they ask about the number of adult tickets, only.

        So, there is no need to work with two unknowns and solve a system of two equations.

        One unknown and one equation is enough, as I will show below in my solution.

        It simplifies the methodology and make calculations/solution/writing shorter.



<pre>
Let x be the number of adult tickets.
Then the number of child tickets was (92-x).


Write an equation for the total revenue

    7.75x + 9.50(92-x) = 837.25.


Simplify and find x

    7.75x + 9.50*92 - 9.50x = 837.25,

    7.75x - 9.50x = 837.25 - 9.50*92,

       -1.75x     =     -36.75,

            x     =     {{{(-36.75)/(-1.75)}}} = 21.


<U>ANSWER</U>.  The number of the child tickets is 21.


<U>CHECK</U>.   Let's check the total revenue:  7.75*21 + 9.50*(92-21) = 837.25.  ! Precisely correct !
</pre>

Solved, using only one unknown and one equation.
Less calculations and shorter writing.