Question

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

Answer 1

Let's denote the number of hot dogs sold as \( h \) and the number of pretzels sold as \( p \). We have the following equations based on the problem:

1. The total number of items sold: \[ h + p = 300 \]

2. The total income needed: \[ 4h + 2p = 800 \]

Now, we can solve these equations step by step.

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

Next, we substitute this expression for \( p \) into the second equation: \[ 4h + 2(300 - h) = 800 \]

Expanding and simplifying: \[ 4h + 600 - 2h = 800 \] \[ 2h + 600 = 800 \] \[ 2h = 800 - 600 \] \[ 2h = 200 \] \[ h = 100 \]

Now that we have \( h \), we can find \( p \): \[ p = 300 - h = 300 - 100 = 200 \]

So, the Baynard High School Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.

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