The movie theater is showing the movie trolls. they charge $5 per ticket for a child and $12 per ticket for an adult. they sell a total of 342 tickets and make a total of $2550. how many of each type of tickets did they sell?

A + c = 342 ... a = 342 - c

12a + 5c = 2550

12 (342 - c) + 5c = 2550

4104 - 12c + 5c = 2550

-12c + 5c = 2550 - 4104

-7c = - 1554

c = - 1554/-7

c = 222

a + c = 342

a + 222 = 342

a = 342 - 222

a = 120

adult tickets sold (a) was 120, child tickets sold (c) was 222