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)

Question

• 250 hot dogs and 50 pretzels
• 100 hot dogs and 200 pretzels
• 200 hot dogs and 100 pretzels
50 hot dogs and 250 pretzels

Answer 1

To solve this problem, we can define two variables: let \( h \) be the number of hot dogs sold, and \( p \) be the number of pretzels sold.

We know two key pieces of information:

1. The total number of hot dogs and pretzels is 300: \[ h + p = 300 \]

2. The total income from selling hot dogs and pretzels is $800: \[ 4h + 2p = 800 \]

Now we will solve these equations step-by-step.

First, we can simplify the second equation: \[ 4h + 2p = 800 \implies 2h + p = 400 \]

Now we have the following system of equations:

1. \( h + p = 300 \)
2. \( 2h + p = 400 \)

Next, we can subtract the first equation from the second to eliminate \( p \): \[ (2h + p) - (h + p) = 400 - 300 \] \[ 2h - h = 100 \] \[ h = 100 \]

Now that we have \( h \), we can plug this back into the first equation to find \( p \): \[ 100 + p = 300 \implies p = 200 \]

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

The answer is:

• 100 hot dogs and 200 pretzels.