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.5*x* + 4*y* = 8
2*x* + 3*y* = 16.50

B.2*x* + 3*y* = 8
5*x* + 4*y* = 16.50

C.2*x* + 5*y* = 8
3*x* + 4*y* = 16.50

D.3*x* + 2*y* = 8
4*x* + 5*y* = 16.50


To determine the correct system of equations, let's break down the given information:

- One family paid **$8.00** for **2 hot dogs** and **3 bags of popcorn**. This gives us 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 us the equation:
  \[
  5x + 4y = 16.50
  \]

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

So, the correct answer is **B**.

Would you like to see the steps for solving this system? 

Here are 5 questions to expand this:

1. How do you solve this system of equations using substitution?
2. How do you solve this system using the elimination method?
3. What would happen if the price of popcorn changed, how would the system change?
4. How would you graph these equations to find the solution visually?
5. Can systems of equations always have a unique solution?

**Tip:** When solving a system of equations, always double-check which variables are assigned to which items (in this case, hot dogs and popcorn).

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

B.2*x* + 3*y* = 8
5*x* + 4*y* = 16.50

C.2*x* + 5*y* = 8
3*x* + 4*y* = 16.50

D.3*x* + 2*y* = 8
4*x* + 5*y* = 16.50

Learn how to solve the system of linear equations for determining the price of hot dogs and popcorn. This problem involves setting up two equations based on real-world transactions and using methods like substitution or elimination to find the solution. Ideal for Grades 7-9 algebra students.

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