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?

Question

Responses

200 hot dogs and 100 pretzels

50 hot dogs and 250 pretzels

100 hot dogs and 200 pretzels

250 hot dogs and 50 pretzels

Answer 1

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

To find this answer, we can set up a system of equations:

Let x represent the number of hot dogs sold.
Let y represent the number of pretzels sold.

From the given information, we know the following:

x + y = 300 (the total number of hot dogs and pretzels)
4x + 2y = 800 (the total income needed)

Solving this system of equations, we can find the values of x and y. By substituting x = 300 - y into the second equation, we have:

4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200

Substituting y = 200 into the first equation, we have:

x + 200 = 300
x = 100

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