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

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

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

100 hot dogs and 200 pretzels

Answer 1

To determine how many hot dogs and pretzels the Baynard High School Boosters need to sell to reach their income goal, we can set up a system of equations based on the information provided.

Let:

• \( x \) = number of hot dogs sold
• \( y \) = number of pretzels sold

From the problem, we have two equations:

1. The total number of hot dogs and pretzels must equal 300: \[ x + y = 300 \]

2. The total income from the sales must equal $800: \[ 4x + 2y = 800 \]

We can solve these equations step by step.

Step 1: Solve the first equation for \( y \): \[ y = 300 - x \]

Step 2: Substitute \( y \) into the second equation: \[ 4x + 2(300 - x) = 800 \] Distributing the \(2\): \[ 4x + 600 - 2x = 800 \] Combine like terms: \[ 2x + 600 = 800 \] Subtract 600 from both sides: \[ 2x = 200 \] Divide by 2: \[ x = 100 \]

Step 3: Substitute \( x \) back into the first equation to find \( y \): \[ y = 300 - 100 = 200 \]

Therefore, the boosters need to sell 100 hot dogs and 200 pretzels.

So, the correct answer is: 100 hot dogs and 200 pretzels.