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
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
250 hot dogs and 50 pretzels
To reach their goal of $800, the Boosters need to sell:
200 hot dogs x $4 = $800
0 pretzels x $2 = $0
So they need to sell 200 hot dogs to reach their goal.
The correct response is:
200 hot dogs and 0 pretzels
incorrect
Apologies for the error. Let's try again.
Let x be the number of hot dogs sold and y be the number of pretzels sold.
The Boosters need to earn a total of $800.
The revenue from hot dogs sold is $4x.
The revenue from pretzels sold is $2y.
Given:
x + y = 300 (total hot dogs and pretzels in stock)
4x + 2y = 800 (total revenue needed)
Solving the equations simultaneously:
From x + y = 300, we get x = 300 - y
Substitute into 4x + 2y = 800:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substitute y = 200 back into x = 300 - y:
x = 300 - 200
x = 100
Therefore, the Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
The correct response is:
100 hot dogs and 200 pretzels.