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

A. 250 hot dogs and 50 pretzels
B. 50 hot dogs and 250 pretzels
C. 200 hot dogs and 100 pretzels
D. 100 hot dogs and 200 pretzels

Answer 1

Let's assume the boosters sell x hot dogs and y pretzels.

The income from selling hot dogs is 4x dollars.
The income from selling pretzels is 2y dollars.

According to the problem, they want to earn a total income of 800 dollars.

So, the equation becomes:
4x + 2y = 800

However, we are also given that there are 300 hot dogs and pretzels in stock. So, the sum of the number of hot dogs and pretzels sold should be equal to 300.

So, the second equation becomes:
x + y = 300

Now we have a system of two equations:
4x + 2y = 800
x + y = 300

Multiplying the second equation by 2, we get:
2x + 2y = 600

Subtracting this equation from the first equation, we get:
2x = 200
x = 100

Substituting x = 100 into the second equation, we get:
100 + y = 300
y = 200

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

The correct answer is option D. 100 hot dogs and 200 pretzels.