The Barnard 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 $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

The Barnard 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 $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?

Answer 1

Let x be the number of hot dogs sold and y be the number of pretzels sold.

We can create a system of equations based on the given information:

1) x + y = 300 (total number of items in stock)
2) 4x + 2y = 800 (total income goal)

Now we can solve the system of equations:

From equation 1:
x = 300 - y

Substitute x into equation 2:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200

Now substitute y = 200 back into x = 300 - y:
x = 300 - 200
x = 100

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