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To solve this problem, we need to create two equations based on the information provided in the question.

Let:
- $ x $ be the price of one hot dog.
- $ y $ be the price of one bag of popcorn.

### Step-by-step breakdown:
1. **First family**: They paid $8.00 for 2 hot dogs and 3 bags of popcorn.
   - This gives us the equation: 
   \[
   2x + 3y = 8
   \]

2. **Second family**: They paid $16.50 for 5 hot dogs and 4 bags of popcorn.
   - This gives us the equation: 
   \[
   5x + 4y = 16.50
   \]

Now, we need to match this system of equations with the answer choices:

- The correct system is $ 2x + 3y = 8 $ and $ 5x + 4y = 16.50 $, which corresponds to **option B**.

Would you like a detailed explanation of how to solve this system of equations? 

Here are 5 follow-up questions related to this:

1. How can we solve this system of equations using the substitution method?
2. How can we solve the same system of equations using the elimination method?
3. What if the prices were in different units? How would that affect the equations?
4. How can we graphically represent the system of equations?
5. How would the problem change if we had a third equation (e.g., for a third family)?

**Tip**: When working with word problems, always define your variables clearly and write down the equations based on the relationships described in the problem.

Hot dogs and bags of popcorn were sold at a concession stand. One family paid $8.00 for 2 hot dogs and 3 bags of popcorn. Another family paid $16.50 for 5 hot dogs and 4 bags of popcorn. Which system of equations can be used to determine the price in dollars of a hot dog, x, and the price in dollars of a bag of popcorn, y?

Learn how to solve a system of equations to find the price of hot dogs and bags of popcorn. This algebra problem uses two linear equations derived from real-life transactions at a concession stand. Suitable for students in Grades 8-10.

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