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?
A.5x + 4y = 8
2x + 3y = 16.50
B.2x + 3y = 8
5x + 4y = 16.50
C.2x + 5y = 8
3x + 4y = 16.50
D.3x + 2y = 8
4x + 5y = 16.50

We can set up a system of equations by using the information provided in the problem:

- One family paid $8.00 for 2 hot dogs and 3 bags of popcorn. This gives the equation:
  \[
  2x + 3y = 8
  \]
  where $ x $ is the price of a hot dog, and $ y $ is the price of a bag of popcorn.

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

Thus, the correct system of equations is:

\[
2x + 3y = 8
\]
\[
5x + 4y = 16.50
\]

The correct answer is **B**.

Would you like more details on how to solve this system of equations? Also, here are 5 related questions for practice:

1. How do you solve a system of equations using substitution?
2. How do you solve a system of equations using elimination?
3. What happens if a system of equations has no solution?
4. How can you check if a solution to a system of equations is correct?
5. How do you solve a system of equations graphically?

**Tip:** When working with systems of equations, it's essential to ensure that each equation is set up correctly from the word problem before solving!

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? A. 5x + 4y = 8, 2x + 3y = 16.50 B. 2x + 3y = 8, 5x + 4y = 16.50 C. 2x + 5y = 8, 3x + 4y = 16.50 D. 3x + 2y = 8, 4x + 5y = 16.50

Learn how to solve a system of equations to find the prices of hot dogs and popcorn. One family paid $8 for 2 hot dogs and 3 bags of popcorn, while another paid $16.50 for 5 hot dogs and 4 bags of popcorn. Suitable for students in Grades 7-10, this problem covers key concepts in algebra and systems of equations.

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