It’s a word problem. Must solve using substitution. I’m not sure how to set it up.
Altogether 568 tickets were sold to a play. An adult ticket cost $5 and $2 for a childrens ticket. Total ticket sales were $2,345. The theater manager expects to sell the same number of each type of ticket for the next production, but wants to increase total sales to$3, 554 by raising adult admission. What is the new cost for the adult ticket?
OK, so call adult ticket a, and child ticket c
a + c = 568 (altogether 568 tickets were sold)
5a + 2c = 2345 (total ticket sales were $2345)
Multiply first equation by 2
2a + 2c = 1136
5a + 2c = 2345
Subtract eq1 from eq 2
2a + 2c = 1136
3a = 1209
a = 403
568 tickets were sold altogether, so, 403 + c = 568
c = 165
This is actually a two part problem. So,
the theater manager wants to keep the child price the same, but increase the adult price so as to get
403 adultprice + 165 $2 = $3554 So,
403 adultprice + $330 = $3554
403 adultprice = $3224
adultprice = 3224/403 = $8.00
The theater manager has to increase the price of an adult ticket to $8.00.