Question 1096650
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Last Tuesday Regal Cinemas sold a total of 8500 movie tickets. Proceeds totalled $64600. 
Tickets can be bought in one of the three ways. A matinee admission costs $5, student admission is $6 all day, 
regular admissions are $8.50. How many of each type were sold if twice as many student tickets were sold as matinee tickets?
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            It is a typical problem to be solved using only one single unknown.



<pre>
Let x be the number of the matinee tickets.

Then the number of the student tickets is 2x,

and the number od the regular admission tickets is  (8500-x-2x) = (8500-3x).


Now you write the total money equation (the revenue)


    5x + 6*(2x) + 8.50*(8500-3x) = 64600  dollars.


Simplify and solve for x


    5x + 12x - 8.50*3*x         = 64600 - 8.50*8500


         x                      = {{{(64600 - 8.50*8500)/(5+12-8.50*3)}}} = 900.


<U>ANSWER</U>.  900 matinee tickets;  2*900 = 1800  student tickets  and the rest, 8500-900-1800 = 5800, were the regular admission tickets.


<U>CHECK</U>.  900*5 + 1800*6 + 5800*8.50 = 64600 dollars, in total.    ! Correct !
</pre>

Solved.


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From my post, learn how to solve such problems using one single unknown variable, only.


It is the major lesson to learn from my solution.