Final answer:
To find out how many adult and children tickets were purchased, we need to use the given information and set up a system of equations. By solving the system using the substitution method, we find that 3 adult tickets and 8 children tickets were purchased.
Step-by-step explanation:
To solve this problem, let's use the given information. We know that the total number of people in the group is 11, and the total amount paid for the tickets was $87. Since the cost for adult tickets is $9 and the cost for children tickets is $7.50, we can set up an equation based on these prices:
x(9) + y(7.50) = 87
where x is the number of adult tickets and y is the number of children tickets. Now we need to solve this equation to find the values of x and y.
Using the given information, we also know that the total number of tickets purchased is 4, so we can write another equation:
x + y = 11
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination.
Let's use the substitution method. We can solve the second equation for one variable and substitute that expression into the other equation. Solving the second equation for x, we get:
x = 11 - y
Now we can substitute this expression for x in the first equation:
(11 - y)(9) + y(7.50) = 87
Expanding and simplifying, we get:
99 - 9y + 7.50y = 87
Combine like terms:
-1.50y = -12
Dividing by -1.50, we find:
y = 8
Substituting this value back into the second equation, we find:
x + 8 = 11
Solving for x, we get:
x = 3
Therefore, 3 adult tickets were purchased and 8 children tickets were purchased.