Question

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

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

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

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

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

Answer 1

To set up the system of equations based on the problem:

- Let \( x \) be the price of a hot dog.
- Let \( y \) be the price of a bag of popcorn.

From the information given:

1. The first family paid $8.00 for 2 hot dogs and 3 bags of popcorn. This gives us the equation:
\[
2x + 3y = 8
\]

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

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

Thus, the answer is:
**d. \( 2x + 3y = 8 \) and \( 5x + 4y = 16.50 \)**.