At her latest concert, she was Bitsy was only able to sell 910 tickets for a total of $15,620 (barely enough to pay her agent). If regular seats cost $18.50 -

Question

And mezzanine seats (the only other option) cost $16.25, how many mezzanine tickets were sold?

Answer 1

First see that there were a total of 910 tickets sold.   There are only 2 types of tickets, the ones that cost $18.50 and the ones that cost $16.25.   Let the $18.50 tickets represent X in this problem.   We do not know how many of each ticket was sold, YET,  but we do know that the X is one amount and the other amount must  be 910-X.  So set this up as $18.50 X  plus the (910-X) times the $16.25   Using distributive property for the terms in parenthesis you multiply each term by the $16.25.  So the equation will be $18.50X+ $16.25(910-X) = $15,620 which was the total profit from sales of all to the tickets.     $18.50X+14,787.50 -16.25X = 15,620.00.  Combine the terms with the Xs to get 2.25X +14,787.50.   = 15,620.00.  Next subtract the 14,787.50 from the 15,620.00 which leaves the equation at 2.25X = 832.50. When you divide by 2.25 you will be left with X=370.   If we had the X representing the tickets that cost $18.50   then 370 of the tickets cost $18.50 and the remaining 540 cost $16.25.   Check your answer and you should get the $15,620.00 profit.    HOpe this helped.