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admission tickets to a motion picture theater were priced at 4 dollars for adults and 3 dollars for students. If 810 tickets were sold and the total receipts were 2853 dollars, how many of each type of ticket weres sold ?

Sagot :

600 adults and 151 students
FINAL ANSWER: 423 tickets sold to adults,  
                               387 tickets sold to students.

SOLUTION:
Let tickets sold to adults: x
      tickets sold to students : y

To rewrite equation in terms of x for tickets sold to students:
                   x + y = 810
                         y = 810 - x

So:  Tickets sold to adults: x   at 4 dollars each
         Tickets sold to students:  810-x   at  3 dollars each

Equation:
   4(x) + 3(810-x) = 2,853
   4x + 2430 - 3x = 2,853
  4x - 3x = 2,853 - 2,430
    x = 423

Number of tickets for each type:
  Adults = x
              = 423 tickets

  Students = 810-x
                   = 810 - 423
                   =  387 tickets

  Add:  423 tickets + 387 tickets = 810 tickets

To check if the total receipts is correct:
     4x + 3 (810-x) = 2,853
     4 (423) + 3 (387) = 2,853
     1,692 + 1,161 = 2,853
                    2,853 = 2,853

 
 
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