lets x = # of children attended the fair
y = # of adults attended the fair
x + y = 1800 so x = 1800 - y
x + 4y = 4800 so x = 4800 - 4y
So now you have
1800 - y = 4800 - 4y
4y - y = 4800 - 1800
3y = 3000
y = 1000
x = 1800 - 1000 = 800
answer:
children: 800 and adults: 1000
double check:
800 + 1000 = 1800 (1800 people enter the fair)
x + 4y = 4800
800 + 4(1000) = 4800
800 + 4000 + 4800
4800 = 4800 ($4800 is collected)