Question

select the correct answer.

the concession stand at the high school football stadium sells hot dogs and hamburgers to raise money for the high school athletic programs. each hot dog sold earns the programs \\$0.50, and each hamburger sold earns \\$0.75. this week, the concession stand sold a combination of 230 hot dogs and hamburgers and earned \\$138.50 for the athletic programs. if \\(x\\) represents the number of hot dogs sold and \\(y\\) represents the number of hamburgers sold, which system of equations represents this situation?

\\(\

$$\begin{aligned} 0.75x + 0.50y &= 138.50 \\\\ x + y &= 230 \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} 0.50x + 0.75y &= 138.50 \\\\ x + y &= 230 \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} 0.75x + 0.50y &= 230 \\\\ x + y &= 138.50 \\end{aligned}$$

\\)

\\(\

$$\begin{aligned} 0.50x + 0.75y &= 230 \\\\ x + y &= 138.50 \\end{aligned}$$

\\)

Explanation:

⚡ Using what you learned: introduction to systems of equations

Step 1: Define variables and total quantity

The problem defines:

• \( x \): number of hot dogs sold
• \( y \): number of hamburgers sold

The total number of items sold is \( 230 \):

$$ x + y = 230 $$

Step 2: Set up the earnings equation

• Each hot dog (\( x \)) earns \( \$0.50 \).
• Each hamburger (\( y \)) earns \( \$0.75 \).
• The total earnings are \( \$138.50 \).

This gives the equation:

$$ 0.50x + 0.75y = 138.50 $$

Step 3: Combine into a system

The system of equations representing this situation is:

$$
LATEXBLOCK0
$$

Answer:

The correct option is the second one:

$$
LATEXBLOCK0
$$