1) c + s + a = 2500
2) 2c + 3s + 5a = 7250
3) s = 2c
substitute eq(3) into eqs (1) and (2):
a) c + 2c + a = 2500 or 3c + a = 2500 or a = 2500 - 3c
b) 2c + 3(2c) + 5a = 7250 or 8c + 5a = 7250
substitute eq(a) into eq(b):
8c + 5(2500 - 3c) = 7250
8c + 12,500 - 15c = 7250
-7c = -5250
c = -5250/-7 = 750
using eq(3):
s = 2(750) = 1500
using eq(1):
750 + 1500 + a = 2500
a = 2500 - 2250 = 250
check using eq(2):
2(750) + 3(1500) + 5(250) = 7250
1500 + 4500 + 1250 = 7250
7250 = 7250
There were 250 adult tickets, 1500 student tickets and 750 childrens tickets sold.