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
200 hot dogs and 100 pretzels
250 hot dogs and 50 pretzels
100 hot dogs and 200 pretzels
Let's say the Boosters sell x hot dogs and y pretzels.
The income from selling hot dogs would be 4x dollars.
The income from selling pretzels would be 2y dollars.
To reach their goal of $800, the equation becomes:
4x + 2y = 800.
Since they have 300 hot dogs and pretzels in stock, the equation also becomes:
x + y = 300.
We can solve this system of equations:
Multiply the second equation by 2:
2x + 2y = 600.
Subtract the second equation from the first:
(4x + 2y) - (2x + 2y) = 800 - 600,
2x = 200,
x = 100.
Plug the value of x back into the second equation:
100 + y = 300,
y = 200.
Therefore, the Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800. Answer: 100 hot dogs and 200 pretzels.
To find out how many hot dogs and pretzels the boosters need to sell, let's set up a system of equations.
Let's say the number of hot dogs sold is represented by "x" and the number of pretzels sold is represented by "y".
Given:
Number of hot dogs: 300
Number of pretzels: 300
Selling price per hot dog: $4
Selling price per pretzel: $2
Income goal: $800
The total income can be calculated as:
Total income = (Number of hot dogs sold × Selling price per hot dog) + (Number of pretzels sold × Selling price per pretzel)
800 = (4x) + (2y)
Also, the total number of hot dogs and pretzels sold should be equal to the total stock:
Total stock = Number of hot dogs sold + Number of pretzels sold
300 = x + y
Now, we can solve this system of equations.
First, let's solve for x in terms of y in the second equation:
x = 300 - y
Substitute this value of x into the first equation:
800 = (4(300 - y)) + (2y)
800 = 1200 - 4y + 2y
800 = 1200 - 2y
2y = 1200 - 800
2y = 400
y = 200
Now we have the value of y, substitute it back into the second equation to find x:
x = 300 - y
x = 300 - 200
x = 100
So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Therefore, the correct answer is:
100 hot dogs and 200 pretzels.
To find the number of hot dogs and pretzels the boosters need to sell, we can set up a system of equations.
Let's denote the number of hot dogs the boosters need to sell as x, and the number of pretzels as y.
We know that each hot dog is sold for $4, so the total income from hot dog sales is 4x.
Similarly, each pretzel is sold for $2, so the total income from pretzel sales is 2y.
The boosters want to earn a total income of $800, therefore we have the equation:
4x + 2y = 800 ........(equation 1)
We also know that the boosters have 300 hot dogs and pretzels in stock. Therefore, another equation we can write is:
x + y = 300 ........(equation 2)
Now we can solve the system of equations to find the values of x and y.
From equation 2, we have x = 300 - y.
Substituting x in equation 1, we get:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
1200 - 2y = 800
-2y = -400
y = 200
Substituting the value of y back into equation 2, we can 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.
So, the correct answer is: 100 hot dogs and 200 pretzels.