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

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

200 hot dogs and 100 pretzels

250 hot dogs and 50 pretzels

50 hot dogs and 250 pretzels

GPT 3.5 · Accepted Answer

To calculate the number of hot dogs and pretzels needed to reach the goal of $800, we can set up a system of equations:

Let x = number of hot dogs sold
Let y = number of pretzels sold

The total earned will be:
4x (for hot dogs) + 2y (for pretzels) = $800

Given that they have a total of 300 hot dogs and pretzels:
x + y = 300

Solving these two equations simultaneously:
4x + 2y = 800
x + y = 300

Multiply the second equation by 2 to align the coefficients of y:
2x + 2y = 600

Subtract the second equation from the first:
2x = 200
x = 100

Now that we know x = 100, plug this back into the second equation to solve for y:
100 + y = 300
y = 200

Therefore, the boosters need to sell 100 hot dogs and 200 pretzels in order to reach their goal of $800. So the correct answer is: 100 hot dogs and 200 pretzels.