Answer:
11 adults
Step-by-step explanation:
First, set up a system of equations:
Let x = number of children and y = number of adults
There is a total of 16 people, so x+y = 16. This is your first equation.
Each child ticket costs $6, so 6x = cost of children's tickets based on the number of children present (x)
Each adult ticket costs $9, so 9y = cost of adult's tickets based on the number of adults present (y)
The total cost of tickets is $129, so 6x+9y = 129. This is your second equation.
Your system of equations is now this:
x + y = 16
6x + 9y = 129
You can solve this system using the method of elimination, where we will eliminate the variable x (number of children), since we are focused on y (number of adults).
Multiply the top equation by -6. This will give the following equation:
-6x - 6y = -96
You can now solve the system of equations by placing the new equation under the second equation like this:
6x + 9y = 129
-6x - 6y = -96
Now, add the two equations together.
6x + (-6x) = 0
9y + (-6y) = 3y
129 + (-96) = 33
After doing this, you get the following equation:
3y = 33
As you can see, the variable x has been eliminated, and you are left with y.
Solve the equation for y:
3y = 33
y = 33/3 = 11
y = 11 adults
