Question 311293
Let x be the number of children.
Let y by the number of adults.

We have to set up two equations:  One is for the number of people and the other is for the amount of money collected.

x + y = 2200
1.50x + 4.00y = 5050

We have to solve this system.  I am going to do it by linear combination, that is, I am going to multiply the top equation by 4, so that, when I subtract the equations, the y's will drop out...here goes

4x + 4y = 8800
-(1.50x + 4.00y = 5050)

which yields

2.5x = 3750
and, then by dividing by 2.5, we get
x = 1500
Now substitute this back into the first equation, and
y = 700