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
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels
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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.