The Baynard High School Boosters are selling hot dogs 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 hot dogs for $4 each and the pretzels for $2 each. How many hot dogs and how many pretzels do the boosters need to sell to reach their goal of $800?(1 point) Responses 200 hot dogs and 100 pretzels 200 hot dogs and 100 pretzels 250 hot dogs and 50 pretzels 250 hot dogs and 50 pretzels 100 hot dogs and 200 pretzels 100 hot dogs and 200 pretzels 50 hot dogs and 250 pretzels

Answer 1

Let's define the number of hot dogs as \( x \) and the number of pretzels as \( y \).

We have two equations based on the given information:

1. The total number of items sold (hot dogs and pretzels) is 300: \[ x + y = 300 \]

2. The total income desired is $800: \[ 4x + 2y = 800 \]

Now we can solve these equations step by step.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 300 - x \]

Now we can substitute \( y \) into the second equation: \[ 4x + 2(300 - x) = 800 \]

Expanding the equation: \[ 4x + 600 - 2x = 800 \]

Combine like terms: \[ 2x + 600 = 800 \]

Now, we can isolate \( 2x \): \[ 2x = 800 - 600 \] \[ 2x = 200 \]

Now divide by 2: \[ x = 100 \]

Now substituting \( x = 100 \) back into the first equation to find \( y \): \[ 100 + y = 300 \] \[ y = 300 - 100 \] \[ y = 200 \]

Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.

The correct answer is: 100 hot dogs and 200 pretzels.