The correct answer is 200 hot dogs and 100 pretzels.
Explanation:
Let x be the number of hot dogs sold and y be the number of pretzels sold. The total income can be represented by the equation 4x + 2y = 800. From the information given, we know that x + y = 300 (since they have 300 items in stock).
We can solve these two equations simultaneously:
4x + 2y = 800
x + y = 300
Multiplying the second equation by 2, we get:
2x + 2y = 600
Subtracting the second equation from the first, we get:
2x = 200
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their income goal of $800.