Question

1. 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?

options:

• $5x + 4y = 8$; $2x + 3y = 16.5$
• $2x + 3y = 8$; $5x + 4y = 16.5$
• $2x + 5y = 8$; $3x + 4y = 16.5$
• $3x + 2y = 8$; $4x + 5y = 16.5$

Explanation:

Step1: Define variables

Let $x$ = price of a hot dog, $y$ = price of a popcorn bag.

Step2: Set first equation (1st family)

2 hot dogs + 3 popcorn = $8.00
$2x + 3y = 8$

Step3: Set second equation (2nd family)

5 hot dogs + 4 popcorn = $16.50
$5x + 4y = 16.5$

Step4: Match to options

The system matches the third option.

Answer:

2x + 3y = 8
5x + 4y = 16.5