825 tickets were sold for a game for a total of $1,462.50. If adult tickets sold for $2.50 and children's tickets sold for $1.00, how many of each kind of ticket were sold?

Let the number of adults tickets = a
Let the number of children’s tickets = c

Form 2 equations:

825 tickets total:
a + c = 825 (1)

Cost of tickets:
2.50a + 1.00c = 1,462.50
c = 1462.50 - 2.5a (2)

Solve equations (1) & (2) simultaneously:

Sub (2) into (1):
a + (1462.5 - 2.5a) = 825
a - 2.5a = -637.5
-1.5a = -637.5
a = 425

Sub a=425 into (1):
425 + c = 825
c = 400

Therefore 450 adults tickets and 400 children’s tickets were sold