Question 1143681
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            This problem is for one single unknown, actually.



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Let x  be the number of tickets purchased at the box office (the unknown value under the question).


Then you have this equation for total money  (the "revenue" equation)


    4.50*180 + 8x = 6*(180 + x).      (1)


Should I explain it in more details ?  --  I think no, since it is quite OBVIOUS: the equation is self-explanatory.


Now simplify the equation and solve it for x :


    810 + 8x = 1080 + 6x

    8x - 6x  = 1080 - 810

    2x       = 270

     x       = 270/2 = 135.


<U>ANSWER</U>.  135 tickets were purchased at the box office.


<U>CHECK</U>.   Left side of the equation (1) is  4.50*180 + 8*135 = 1890 dollars.

         Right side of the equation (1) is  6*(180 + 135) = 1890 dollars.

         Both sides of the equation (1) are equal.

         It means that the solution and the answer are CORRECT (!)
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Solved.