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 50 hot dogs and 250 pretzels 50 hot dogs and 250 pretzels 250 hot dogs and 50 pretzels 250 hot dogs and 50 pretzels 100 hot dogs and 200 pretzels 100 hot dogs and 200 pretzels 200 hot dogs and 100 pretzels
To reach their goal of $800, the boosters need to sell a combination of hot dogs and pretzels. Let x be the number of hot dogs sold and y be the number of pretzels sold.
The total income can be calculated as:
Total income = 4x (selling price of hot dogs) + 2y (selling price of pretzels)
Given that the boosters want to earn $800, the equation becomes:
4x + 2y = 800
Also, the boosters have 300 hot dogs and pretzels in stock, so:
x + y = 300
Solving these two equations simultaneously will give us the number of hot dogs and pretzels needed to reach the goal of $800.
4x + 2y = 800
x + y = 300
Multiplying the second equation by 2 and subtracting it from the first equation:
4x + 2y = 800
- 2x - 2y = 600
2x = 200
x = 100
So, the boosters need to sell 100 hot dogs and can sell the remaining 200 pretzels to reach their goal of $800.
Therefore, the correct response is: 100 hot dogs and 200 pretzels.