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

200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels

100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels

250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels

50 hot dogs and 250 pretzels

Answer 1

Let \( h \) represent the number of hot dogs sold and \( p \) represent the number of pretzels sold. We are given two equations based on the problem:

1. The total number of items (hot dogs and pretzels) must equal 300:
\[
h + p = 300
\]

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

Now we can solve this system of equations.

First, we can simplify the second equation. Divide the entire equation by 2:
\[
2h + p = 400
\]

Now we have the simpler set of equations:
1. \( h + p = 300 \) (1)
2. \( 2h + p = 400 \) (2)

Next, we'll solve for \( p \) in equation (1):
\[
p = 300 - h
\]

Now we can substitute this expression for \( p \) into equation (2):
\[
2h + (300 - h) = 400
\]
\[
2h + 300 - h = 400
\]
\[
h + 300 = 400
\]
\[
h = 400 - 300
\]
\[
h = 100
\]

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

So, the boosters need to sell:
- **100 hot dogs** and **200 pretzels**.

Looking at the responses, the correct one is:
**100 hot dogs and 200 pretzels.**