The Baynard High School Boosters are selling hotdogs and pretzels at the concession stand. They have 300 hot dogs and pretzels in stock and want to earn an income of $800. They plan to sell the hotdogs for $4 each and the pretzels for $2 each. How many hotdogs and how many pretzels do the boosters need to sell reach their goal of $800?

Answer 1

Let \( x \) be the number of hot dogs sold and \( y \) be the number of pretzels sold.

We have the following two equations based on the problem description:

1. Total items sold: \[ x + y = 300 \]

2. Total income generated: \[ 4x + 2y = 800 \]

Now, we can solve this system of equations.

First, we can simplify the second equation by dividing everything by 2: \[ 2x + y = 400 \]

Now we have the simplified system:

1. \( x + y = 300 \)
2. \( 2x + y = 400 \)

Next, we can subtract the first equation from the second: \[ (2x + y) - (x + y) = 400 - 300 \] \[ 2x + y - x - y = 100 \] \[ x = 100 \]

Now that we found \( x \), we can substitute it back into the first equation to find \( y \): \[ 100 + y = 300 \] \[ y = 300 - 100 \] \[ y = 200 \]

Thus, the boosters need to sell:

• Hot dogs: \( \mathbf{100} \)
• Pretzels: \( \mathbf{200} \)

To verify, we can check the income:

• Income from hot dogs: \( 100 \times 4 = 400 \)
• Income from pretzels: \( 200 \times 2 = 400 \)
• Total income: \( 400 + 400 = 800 \), which matches the goal.

Therefore, the final answer is: They need to sell 100 hot dogs and 200 pretzels.