Admission tickets to the local Nutcracker production cost $2.50 for children and $3.50 for adults. The price for 8 tickets was $23.00. How many adult and children tickets were purchased?

a + c = 8

3.5a + 2.5c = 23

Now just solve for a and c.

Let's assume that the number of children tickets purchased is x.

Therefore, the number of adult tickets purchased would be 8 - x (since 8 tickets were purchased in total).

The cost of the children tickets would be 2.50 * x, and the cost of the adult tickets would be 3.50 * (8 - x).

According to the given information, the total cost of the tickets was $23.00. So, we can write the equation:

2.50x + 3.50(8 - x) = 23

Now, let's solve this equation:

2.50x + 28 - 3.50x = 23
-1x = 23 - 28
-1x = -5

Multiplying both sides of the equation by -1, we get:

x = 5

So, 5 children tickets were purchased.
And, the number of adult tickets would be 8 - 5 = 3.

Therefore, 5 children tickets and 3 adult tickets were purchased.

To solve this problem, let's let "x" represent the number of children's tickets and "y" represent the number of adult tickets.

According to the information given, each child's ticket costs $2.50, so the total cost of the children's tickets is 2.50x. Similarly, each adult ticket costs $3.50, so the total cost of the adult tickets is 3.50y.

The problem also states that the price for 8 tickets was $23.00. This implies that the total cost of the children's and adult tickets combined is $23.00.

Thus, we can write the equation: 2.50x + 3.50y = 23.00.

Now, we need to find values for "x" and "y" that satisfy this equation. We can do this by considering the given information that there were a total of 8 tickets purchased.

So, we can write another equation based on the total number of tickets: x + y = 8.

Now, we have a system of two equations with two variables:

2.50x + 3.50y = 23.00
x + y = 8

To solve this system, we can use substitution or elimination. In this case, let's solve it using elimination.

First, multiply the second equation by -2.50 to cancel out the x variable:

-2.50(x + y) = -2.50(8)
-2.50x - 2.50y = -20

Now, add this equation to the first equation:

2.50x + 3.50y + (-2.50x - 2.50y) = 23.00 + (-20)
y = 3.00

Now, substitute the value of y = 3 into the second equation:

x + 3 = 8
x = 5

Therefore, 5 children's tickets and 3 adult tickets were purchased.