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 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 50 hot dogs and 250 pretzels
Let's use a system of equations to solve this problem. Let x represent the number of hot dogs sold and y represent the number of pretzels sold.
From the problem statement, we know that the boosters want to earn a total income of $800. We can express this as an equation: 4x + 2y = 800.
We also know that the boosters have 300 hot dogs and pretzels in stock. This can be expressed as a second equation: x + y = 300.
To solve this system of equations, we can use substitution or elimination.
Let's use elimination. Multiply the second equation by -2 to make the coefficients of y the same: -2(x + y) = -2(300), which simplifies to -2x - 2y = -600.
Now we can add the two equations together to eliminate the y variable: 4x + 2y + -2x - 2y = 800 + -600.
Simplifying the equation, we get: 2x = 200.
Dividing both sides by 2, we find that: x = 100.
Substituting this value back into one of the original equations, we can solve for y: 100 + y = 300.
Simplifying the equation, we get: y = 200.
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
To find out how many hot dogs and pretzels the boosters need to sell to reach their goal of $800, we can set up the following equations:
Let x = number of hot dogs sold
Let y = number of pretzels sold
The income from selling hot dogs can be calculated as 4x, and the income from selling pretzels can be calculated as 2y. The total income earned must be equal to $800, so we have the equation:
4x + 2y = 800
Next, we need to consider the stock of hot dogs and pretzels available. The boosters have a total of 300 hot dogs and pretzels in stock, so we have the equation:
x + y = 300
We now have a system of equations to solve:
4x + 2y = 800
x + y = 300
One way to solve the system is by substitution. We can solve the second equation for x and substitute it into the first equation:
x = 300 - y
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substituting this value of y back into the second equation, we can solve for x:
x + 200 = 300
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
To get the answer to this question, we need to set up a system of equations.
Let's assume the number of hot dogs sold is represented by "H" and the number of pretzels sold is represented by "P".
The income equation can be written as: 4H + 2P = 800. (since each hot dog is sold for $4 and each pretzel for $2)
We also know that the total number of hot dogs and pretzels in stock is 300, so we can write the equation: H + P = 300.
Now we can solve these equations to find the values of H and P.
One way to solve is by substitution or elimination.
We can solve by elimination, so let's multiply the second equation by 2 to make the coefficients of H equal:
2H + 2P = 600.
Now we can subtract the second equation from the first:
(4H + 2P) - (2H + 2P) = 800 - 600
2H = 200
H = 100.
Now, substitute the value of H into either of the original equations (let's use the second one):
100 + P = 300
P = 200.
Therefore, the Boosters need to sell 100 hot dogs and 200 pretzels to reach their income goal of $800.
So, the correct answer is 100 hot dogs and 200 pretzels.