We will begin by naming our variables:
x = number of children
y = number of adults
The number of children (x) plus the number of adults (y) equals the total number of visitors (295).
x + y = 295 Equation 1
The amount collected from children is the number of children times the cost per child (3.75x). The amount collected from adults is the number of adults times the cost per adult (6.4y).
The amount collected from children (3.75x) plus the amount collected from adults (6.4y) equals the total amount collected (1464).
3.75x + 6.4y = 1464 Equation 2
Now that we have 2 equations with 2 variables, we can use substitution to solve the problem.
x + y = 295 Equation 1
x + y  y = 295  y Subtract y from each side
x = 295  y Simplify
3.75x + 6.4y = 1464 Equation 2
3.75(295  y) + 6.4y = 1464 Substitute the value of x from equation 1 into equation 2
1106.25  3.75y + 6.4y = 1464 Distribute the 3.75
1106.25 + 2.65y = 1464 Simplify
1106.25 + 2.65y  1106.25 = 1464  1106.25 Subtract 1106.25 from each side
2.65y = 357.75 Simplify
2.65y/2.65= 357.75/2.65 Divide both sides by 2.65
y = 135 Simplify
x = 295  y Equation 1 solved for x
x = 295  135 Substitute the value of y
x = 160 Simplify
There were 160 children and 135 adults admitted to the amusement park.
2/13/2013

John R.