Question 103103
Ok first set some variables.
Lets call adults x
Lets call children y
Given: 2200 people attend the fair
using x and y write and equation to express this 
x + y = 2200
Now lets look at what else we are told
Given: Child admission fee is $1.50
Adult admission fee is $4.00
The total amount collected is $5050.00
Now again using x and y write and equation to express this known information
4x + 1.5y = 5050
In other words $4 times the number of adults (x) plus $1.50 times the number of children (y) equals $5050
Ok so now we have a system of equations that we can use to solve for x and y
x + y = 2200
AND
4x + 1.5y = 5050
To solve the equations I will demonstrate the substitution method.
Take the first equation and set it equal to x
x + y = 2200
subtract y from both sides
x + y - y = 2200 - y
x = 2200 - y
Now since we have shown that x equals 2200-y we can substitute that for x in the second equation and solve for y
4x + 1.5y = 5050
4(2200-y) + 1.5y = 5050
multiply 4 across (2200-y)
8800 - 4y + 1.5y = 5050
combine like terms
8800 - 2.5y  = 5050
subtract 8800 from both sides
8800 - 8800 - 2.5y  = 5050 - 8800
-2.5y  = -3750
divide both sides by -2.5
-2.5y/-2.5  = -3750/-2.5
y = 1500
<b>Answer: 1500 children attended the fair</b>
Now use this answer to find x
Take the first equation and substitute y with 1500
x + y = 2200
x + 1500 = 2200
subtract 1500 from both sides
x + 1500 - 1500 = 2200 - 1500
x = 700
<b>Answer: 700 adults attended the fair</b>
Check both answers in both equations
first equation:
x + y = 2200
700 + 1500 = 2200
2200 = 2200
Now the second equation:
4x + 1.5y = 5050
4(700) + 1.5(1500) = 5050
2800 + 2250 = 5050
5050 = 5050