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?

Question

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 \( 5x + 4y = 16.50 \).