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The admission fee at an amusement park is $3.75 for children and $6.40 for adults.

The admission fee at an amusement park is $3.75 for children and $6.40 for adults. On a certain day, 295 people entered the park, and the admission fees collected totaled 1464 dollars. How many children and how many adults were admitted?

number of children equals
number of adults equals

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1 Answer

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.