Question

University Theater sold 556 tickets for a play. Tickets cost $22 per adult
and $12 per senior citizen. If total receipts were $8492, how many senior
citizen tickets were sold?

Answer 1

Let A be number of adult tickets brought
Let S be number of senior citizen tickets brought

8492 = 22A + 12S (1)
A = 556 - S (2)

Plug (2) into (1)
8492 = 22(556 - S) + 12S
8492 = 12232 - 22S + 12S
8492 - 12232 = -22S + 12S
-3740 = -10S
-3740/10 = -10S/-10
374 = S
S = 374

Note that there are several more steps you can take to check the answer and/or find A.