https://file.aiquickdraw.com/mathbot/file/1726624443587yzdfuy0h.jpg

The problem asks us to determine how many tickets need to be purchased so that the total cost for both Carnival A and Carnival B will be the same.

Let's break down the cost structure for each carnival:

- **Carnival A:**
  - Entrance fee: $5.00
  - Ticket price: $0.65 per ticket

- **Carnival B:**
  - Entrance fee: $10.00
  - Ticket price: $0.45 per ticket

We need to write an equation where the total cost of Carnival A equals the total cost of Carnival B. 

Let $ x $ represent the number of tickets purchased.

- **Total cost at Carnival A**: 
  \[
  \text{Cost of Carnival A} = 5.00 + 0.65x
  \]

- **Total cost at Carnival B**: 
  \[
  \text{Cost of Carnival B} = 10.00 + 0.45x
  \]

Set these two costs equal to each other:

\[
5.00 + 0.65x = 10.00 + 0.45x
\]

Now, let's solve for $ x $.

\[
0.65x - 0.45x = 10.00 - 5.00
\]

\[
0.20x = 5.00
\]

\[
x = \frac{5.00}{0.20} = 25
\]

Thus, the number of tickets needed for the total cost to be the same is **25**. The correct answer is **a. 25**.

Would you like more details or have any questions?

Here are some related questions:
1. What would the total cost be if you purchased 10 tickets at each carnival?
2. How would the equation change if Carnival A raised its entrance fee to $6.00?
3. What if Carnival B reduced the ticket price to $0.40? How would that affect the solution?
4. How can we generalize this equation for different entrance fees and ticket prices?
5. What does the solution represent in terms of the relationship between the ticket prices and entrance fees?

**Tip:** Always isolate the variable on one side of the equation to simplify solving linear equations.

Carnival A charges an entrance fee of $5.00 per person and $0.65 per ticket for the rides. Carnival B charges an entrance fee of $10.00 per person and $0.45 per ticket for the rides. Write and solve an equation to determine how many tickets can be purchased in order for the total cost at Carnival A and Carnival B to be the same?

Learn how to solve a linear equation where Carnival A charges $5.00 entrance fee and $0.65 per ticket, while Carnival B charges $10.00 entrance fee and $0.45 per ticket. Find out how many tickets make the total cost equal at both carnivals. Suitable for Grades 7-9.

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