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?

Select {responseValue}
5 X plus 4 Y equals 8... 2 X plus 3 Y equals sixteen point 5

Select {responseValue}
2 X plus 3 Y equals 8... 5 X plus 4 Y equals sixteen point 5

Select {responseValue}
2 x plus 5 Y equals 8... 3 X plus 4 Y equals sixteen point 5

Select {responseValue}
3 X plus 2 Y equals 8... 4 X plus 5 Y equals sixteen point 5

Answer 1

To formulate a system of equations from the given problem, let's denote the price of a hot dog as \( x \) and the price of a bag of popcorn as \( y \).

From the information provided:

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

2. The second family paid $16.50 for 5 hot dogs and 4 bags of popcorn. This can be represented by the equation:
\[
5x + 4y = 16.5
\]

Thus, the system of equations that can be used to determine the prices of hot dogs and popcorn is:
\[
\begin{cases}
2x + 3y = 8 \\
5x + 4y = 16.5
\end{cases}
\]

Among the options provided, the correct choice is:
**2 X plus 3 Y equals 8... 5 X plus 4 Y equals sixteen point 5**.