Atheater received $8,917 in ticket sales for one performance of a play. tickets for preferred seats cost $45 each and regular seats cost $34 each. all of the theaters 75? preffered seats were sold out that evening. how many tickets were sold?

Let
P = Number of ticket for preferred seats costing $45 per seat
R = Number of regular seats costing $34 per seat.

Total revenue = P*45 + R*34 =8,917

45P + 34R = 8917

But, number of preferred seats is 75 or P=75 seats
Then,
45*75 +34R = 8917
3375 +34R = 8917
34R = 5542
R = 5542/34 = 163

Total number of seats = P+R = 75+163 = 238 seats. If each seat is sold for one ticket, then 238 tickets wee sold.