The baynard high School boosters are selling hot dogs and pretzels at the concession stand. They have 300 hot dogs and pretzels and 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? 50 hot dogs and 250 pretzels, 250 hot dogs and 50 pretzels, 100 hot dogs and 200 pretzels or 200 hot dogs and 100 pretzels
Let's assume the boosters sell x hot dogs and y pretzels.
The hot dogs are sold for $4 each, so the revenue from selling hot dogs is 4x.
The pretzels are sold for $2 each, so the revenue from selling pretzels is 2y.
The total revenue from selling both hot dogs and pretzels is the sum of the revenue from selling hot dogs and pretzels, which is 4x + 2y.
We need to find the values of x and y that satisfy the equation 4x + 2y = 800.
Using trial and error, we can check each option:
1. 50 hot dogs and 250 pretzels:
Revenue from hot dogs = 4 * 50 = $200
Revenue from pretzels = 2 * 250 = $500
Total revenue = $200 + $500 = $700 (not enough to reach $800)
2. 250 hot dogs and 50 pretzels:
Revenue from hot dogs = 4 * 250 = $1,000
Revenue from pretzels = 2 * 50 = $100
Total revenue = $1,000 + $100 = $1,100 (more than $800)
3. 100 hot dogs and 200 pretzels:
Revenue from hot dogs = 4 * 100 = $400
Revenue from pretzels = 2 * 200 = $400
Total revenue = $400 + $400 = $800 (exact amount needed)
4. 200 hot dogs and 100 pretzels:
Revenue from hot dogs = 4 * 200 = $800
Revenue from pretzels = 2 * 100 = $200
Total revenue = $800 + $200 = $1,000 (more than $800)
Therefore, the correct answer is 100 hot dogs and 200 pretzels.