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Let's analyze the problem step by step.

We are given two scenarios:
1. One family paid $8.00 for 2 hot dogs and 3 bags of popcorn.
2. Another family paid $16.50 for 5 hot dogs and 4 bags of popcorn.

We need to create a system of equations to represent these situations. Let:
- $ x $ represent the price of one hot dog,
- $ y $ represent the price of one bag of popcorn.

### Writing the equations:
1. For the first family: 
   \[
   2x + 3y = 8
   \]
   (2 hot dogs + 3 bags of popcorn = $8)

2. For the second family:
   \[
   5x + 4y = 16.50
   \]
   (5 hot dogs + 4 bags of popcorn = $16.50)

Now, let's check the options:
- **A**: $ 5x + 4y = 8 $, and $ 2x + 3y = 16.50 $ — This option reverses the two totals and is incorrect.
- **B**: $ 2x + 3y = 8 $, and $ 5x + 4y = 16.50 $ — This matches our equations, so it is **correct**.
- **C**: The equations are $ 2x + 5y = 8 $ and $ 3x + 4y = 16.50 $, which do not match the given problem.
- **D**: The equations are $ 3x + 2y = 8 $ and $ 4x + 5y = 16.50 $, which also do not match the problem.

### Correct Answer:
The correct system of equations is option **B**:
\[
2x + 3y = 8 \quad \text{and} \quad 5x + 4y = 16.50
\]

Would you like a detailed breakdown of how to solve these equations to find the values of $ x $ and $ y $? 

Here are 5 related questions to deepen your understanding:
1. How would you solve the system of equations using substitution?
2. Can you solve the system using the elimination method?
3. What if a third family paid $12 for 3 hot dogs and 2 bags of popcorn? How would you adjust the system?
4. How can you interpret the solution to this system in terms of price comparison?
5. What if the prices were discounted by 10%? How would that affect the system?

**Tip**: When setting up equations, always verify that your terms and coefficients match the quantities in the word 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 determine the price of hot dogs and popcorn. Given the costs for different family purchases, this problem explores the use of algebraic methods such as substitution and elimination to find the correct solution.

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