The baynard high school boosters are selling hotdogs and pretzels at the concession stand. They have 300 hotdogs and pretzels in stock and want to earn an income of $800. They plan to sell the hotdogs for four dollars each and the pretzels for two dollars each how many hotdogs and how many pretzels did the boosters need to sell to reach their goal of $800?
Let H be the number of hotdogs and P be the number of pretzels the boosters need to sell.
We know that H + P = 300 and 4H + 2P = $800.
We can multiply the second equation by 2 and subtract it from the first equation to eliminate P: 2H + 4P - 4H - 2P = $600
This simplifies to 2P = $600.
Therefore, the boosters need to sell 300 - P hotdogs to reach their goal. We substitute this into the second equation to find the number of hotdogs sold: 4(300 - P) + 2P = $800
Expanding the parentheses, we get 1200 - 4P + 2P = $800
Combining like terms, we get -2P = -$400
Dividing both sides by -2, we find that P = $200
Therefore, the boosters need to sell 300 - 200 = <<300-200=100>>100 hotdogs to reach their goal. Answer: \boxed{100}.