The Barnard 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
A. 50 hot dogs and 250 pretzels
B. 250 hot dogs and 59 pretzels
C. 200 hot dogs and 100 pretzels
D. 100 hot dogs and 200 pretzels
Let's assume the number of hot dogs sold is x, and the number of pretzels sold is y. From the given information, we can set up the following equations:
4x + 2y = 800 (equation 1)
x + y = 300 (equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.
Solve equation 2 for x:
x = 300 - y
Substitute this expression for x into equation 1:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substitute the value of y into equation 2 to find x:
x + 200 = 300
x = 300 - 200
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800. The answer is D.