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The admission fee at an amusement park is $1.75 for children and $5.60 for adults. On a certain day, 340 people entered the park, and the admission fees collect

The admission fee at an amusement park is $1.75 for children and $5.60 for adults. On a certain day, 340 people entered the park, and the admission fees collected totaled 1288 dollars. How many children and how many adults were admitted?

number of children equals
number of adults equals

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2 Answers

Hi there, Treena!  To solve this problem, set up the following equation:

1.75x + 5.60y = 1288, where x is the number of children (multiplied by the kid rate of $1.75) and y is the number of adults (multiplied by the adult rate of $5.60)

You will need a second equation: x + y = 340.

Let's solve the second equation for x first.  Subtract y from both sides and you get x = 340 - y.  Great!  Now you have an equation for x, which you can plug into the first equation.  The first equation is:

1.75x + 5.60y = 1288

Now you are substituting 340 - y for x in this equation to get:

1.75(340 - y) + 5.60y = 1288

Now let's use the distributive property to get: 595 - 1.75y + 5.60y = 1288

Let's add -1.75y + 5.60y to get:

595 + 3.85y = 1288

Subtract 595 from both sides to get:

3.85y = 693

Divide both sides by 3.85 and we get y = 180.  Remember that y equals the number of adults.  There were 180 adults at the amusement park.

Now we need to see how many kids were at the amusement park.  Let's look at that second equation again:

x + y = 340

Now we know y, so let's plug it in:

x + 180 = 340

Subtract 180 from both sides and we get:

x = 160.  There were 160 kids and 180 adults at the amusement park. 

I would have thought there would be more kids!  But I guess adults like roller coasters too!

x = Number of children

y = Number of adults

Then number of children (x) plus the number of adults (y) equals 340.

x + y = 340                Equation 1

The amount collected from children's tickets (1.75x) plus the amount collected from adult tickets (5.6y) equals the total amount collected 1288.

1.75x + 5.6y = 1288    Equation 2

Either substitution or elimination can be used to solve the system.  I will use substitution.

x + y = 340                                      Equation 1

x + y - y = 340 - y                             Subtract y from each side

x = 340 - y                                        Simplify

1.75x + 5.6y = 1288                           Equation 2

1.75(340 - y) + 5.6y = 1288                Substitute x from equation 1 into equation 2

595 - 1.75y + 5.6y = 1288                  Distribute the 1.75

595 + 3.85y = 1288                            Simplify

595 + 3.85y - 595 = 1288 - 595           Subtract 595 from each side

3.85y = 693                                       Simplify

3.85y/3.85 = 693/3.85                        Divide each side by 3.85

y = 180                                             Simplify

x = 340 -y                                         Equation 1 solved for x

x = 340 - 180                                    Substitution

x = 160                                             Simplify

The amusement park sold 160 child tickets and 180 adult tickets.