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

Question

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

Answer 1

Hi Treena,

Let us assume that the number of children who entered the park is x.

Now, we know that 295 people entered the park on a certain day. Which means the number of adults who entered the park is (295 - x). You want to interpret this as, off the 295 people who entered the park on a given day, we know that x of them were children. Therefore, the balance must be adults.

Therefore, we have

Number of children who entered the park = x

Number of adults who entered the park = 295 - x

The fee for children is $3.75 and for adults is $6.40.

Therefore, total amount that x children paid to enter the park is $3.75 * x

and, total amount that adults paid to enter the park is $6.40 * (295 - x) = 1888 - 6.40 * x.

Therefore, combining the two amounts we will have the total admission fees collected. That is,

(Total amount paid by children) + (Total amount paid by adults) = Total admission fees collected.

Putting our numbers,

(3.75 * x) + (1888 - 6.40 * x) = 1464. 

The expression on the left hand side will simplify to 1888 - (6.40 * x) + (3.75 * x). Combining the x term coefficients we have -6.40 + 3.75 = 2.65.

The expression on the left hand side simplifies to 1888 - 2.65 * x and is equal to 1464.

That is, 1888 - 2.65 * x  = 1464. Let us move the 1464 to the left hand side and move the 2.65 * x term to the right. Since we are moving them to opposite sides of the equation, each term will reverse sign.

Therefore, now 1888 - 1464 = 2.65 * x. Or, 424 = 2.65*x.

Dividing both sides by 2.65, gives us (424 / 2.65) = (2.65 / 2.65)*x

Or, 160 = x. Therefore, 160 children entered the park. And (295 - x) adults entered the park - or, (295 - 160)  adults - which is 135 adults.

Therefore, number of children = 160 and number of adults = 135

I hope this helps

Answer 2

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.