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
100 hot dogs and 200 pretzels
50 hot dogs and 250 pretzels
250 hot dogs and 50 pretzels
200 hot dogs and 100 pretzels
Let's assume the boosters sell x hot dogs and y pretzels.
The total income from selling hot dogs is 4x.
The total income from selling pretzels is 2y.
Since the boosters want to earn a total income of $800, we can set up the equation:
4x + 2y = 800.
We also know that the boosters have a stock of 300 hot dogs and pretzels, so we can set up another equation:
x + y = 300.
To solve this system of equations, we can use the substitution method.
First, solve the second equation for x:
x = 300 - y.
Now substitute this expression for x into the first equation:
4(300 - y) + 2y = 800.
Simplify and solve for y:
1200 - 4y + 2y = 800,
-2y = -400,
y = 200.
Now substitute this value of y back into the second equation to solve for 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.
To find the number of hot dogs and pretzels the boosters need to sell to reach their goal of $800, we can set up a system of equations.
Let's denote the number of hot dogs as "x" and the number of pretzels as "y."
According to the given information:
The selling price of a hot dog is $4, so the total income from selling hot dogs is 4x.
The selling price of a pretzel is $2, so the total income from selling pretzels is 2y.
The total income from selling both is $800, so we have the equation:
4x + 2y = 800.
We also know that the boosters have 300 hot dogs and pretzels combined in stock, so:
x + y = 300.
Now we can solve this system of equations to find the values of x and y.
Using the method of substitution, we can solve the second equation for x:
x = 300 - y.
Substituting this value into the first equation:
4(300 - y) + 2y = 800.
Expanding and simplifying:
1200 - 4y + 2y = 800,
-2y = -400,
y = 200.
Substituting this value back into the second equation to find x:
x + 200 = 300,
x = 100.
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
To determine how many hot dogs and pretzels the boosters need to sell to reach their goal of $800, we can set up a system of equations.
Let's use the variables "x" to represent the number of hot dogs sold and "y" to represent the number of pretzels sold.
According to the information given, the boosters plan to sell the hot dogs for $4 each and the pretzels for $2 each. Therefore, the income generated from selling hot dogs can be represented by 4x, and the income generated from selling pretzels can be represented by 2y.
The boosters want to reach a total income of $800, so we can set up the equation:
4x + 2y = 800
Additionally, we are told that there are a total of 300 hot dogs and pretzels in stock. This gives us another equation:
x + y = 300
Now we have a system of two equations:
4x + 2y = 800
x + y = 300
We can solve this system of equations to find the values of x and y, which represent the number of hot dogs and pretzels sold, respectively.
One way to solve this system is by substitution. Let's solve for x in terms of y in the second equation:
x = 300 - y
Now substitute this expression for x in the first equation:
4(300 - y) + 2y = 800
Simplify the equation:
1200 - 4y + 2y = 800
-2y = 800 - 1200
-2y = -400
Divide both sides by -2 to solve for y:
y = (-400) / (-2)
y = 200
Now substitute the value of y back into the second equation to solve for 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. So the correct answer is:
100 hot dogs and 200 pretzels.