Hi, 

 270 tickets were sold       

Let x and (270-x) represent the number of adult and student tickets respectively

Question States***

 $6*x + $4.50(270-x) = $1590

solving for x

  6x + 4.50*270 - 4.50x = 1590

       1.50x = 1590 - 1215

       1.50x = 375

           x = 250, the number of adult tickets.  Student tickets = 20



CHECKING our Answer***

   $6*250 + 20*$4.50 = $1590 

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