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The problem asks which system of equations can be used to determine the price of a hot dog $x$ and the price of a bag of popcorn $y$.

Let's analyze the given information:

1. One family paid $8.00 for 2 hot dogs and 3 bags of popcorn. This can be expressed as the equation:
   \[
   2x + 3y = 8
   \]
   (where $x$ is the price of one hot dog, and $y$ is the price of one bag of popcorn).

2. Another family paid $16.50 for 5 hot dogs and 4 bags of popcorn. This can be expressed as the equation:
   \[
   5x + 4y = 16.50
   \]

So, the correct system of equations is:
\[
\begin{aligned}
    2x + 3y &= 8 \\
    5x + 4y &= 16.50
\end{aligned}
\]

Looking at the options, **Option B** matches this system of equations.

Would you like further clarification or a breakdown of any part of the problem? 

Here are 5 follow-up questions to deepen your understanding:
1. How do you solve a system of equations by substitution or elimination?
2. What happens if the two equations in a system are parallel?
3. Can you solve this system of equations using a graph?
4. How do you interpret the solution of this system in the context of the problem?
5. Can systems of equations have more than one solution?

**Tip**: When solving systems of equations, always check that each equation correctly represents the given scenario before choosing the method to solve them.

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 a hot dog and a bag of popcorn, given two scenarios where families paid $8.00 and $16.50. This problem covers key algebraic concepts of linear equations and is suitable for students in Grades 7-10.

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