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?

Group of answer choices

2x + 3y = 8
5x + 4y = 16.50

5x + 4y = 8
2x + 3y = 16.50

3x + 2y = 8
4x + 5y = 16.50

2x + 5y = 8
3x + 4y = 16.50

To solve this problem, we need to write a system of equations that reflects the information given about the purchases made by two families.

### Breakdown:
- The first family paid $8.00 for 2 hot dogs and 3 bags of popcorn. This translates to the equation:
  \[
  2x + 3y = 8
  \]
  where $x$ is the price of one hot dog and $y$ is the price of one bag of popcorn.

- The second family paid $16.50 for 5 hot dogs and 4 bags of popcorn. This translates to the equation:
  \[
  5x + 4y = 16.50
  \]

Thus, the correct system of equations that represents this situation is:
\[
\boxed{2x + 3y = 8 \quad \text{and} \quad 5x + 4y = 16.50}
\]

### Answer:
The correct choice is:
\[
2x + 3y = 8 \quad \text{and} \quad 5x + 4y = 16.50
\]

Would you like to see a step-by-step solution for solving this system of equations?

### Follow-up questions:
1. How do you solve a system of linear equations using substitution?
2. How do you solve a system of linear equations using elimination?
3. What are the potential methods to check the solution of a system of equations?
4. What happens if two equations in a system are multiples of each other?
5. How can you graphically solve a system of linear equations?

### Tip:
When setting up systems of equations, always make sure each variable corresponds to the same quantity in both equations, such as prices in this case.

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 linear equations to determine the price of hot dogs and bags of popcorn. The problem includes the equations 2x + 3y = 8 and 5x + 4y = 16.50. Ideal for students in Grades 7-9, this example covers algebraic concepts and system of equations solutions.

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