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
100 hot dogs and 200 pretzels
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels
200 hot dogs and 100 pretzels
To reach their goal of $800, the boosters can calculate the number of hot dogs and pretzels they need to sell using the following equations:
$4 * number of hot dogs + $2 * number of pretzels = $800
Let's solve for the unknowns. We have two variables (number of hot dogs and number of pretzels) and two equations, so we can solve the system of equations.
From the first equation, we can rewrite it as:
4H + 2P = 800
Since we know they have a total of 300 hot dogs and pretzels in stock:
H + P = 300
Now we can use substitution or elimination method to solve this system of equations. Let's use substitution.
From the second equation, we can rewrite it as:
P = 300 - H
Substitute this value into the first equation:
4H + 2(300 - H) = 800
4H + 600 - 2H = 800
2H = 200
H = 100
Now substitute the value of H into the equation we found in the second step:
P = 300 - 100
P = 200
So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800. Thus, the correct answer is:
100 hot dogs and 200 pretzels
To find the number of hot dogs and pretzels the boosters need to sell, let's assume they 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.
Since they want to earn a total income of $800, we can set up the equation:
4x + 2y = 800
Also, we know that the boosters have a total of 300 hot dogs and pretzels in stock, so we can also set up the equation for the total quantity:
x + y = 300
We now have a system of equations:
4x + 2y = 800
x + y = 300
To solve this system, we can use any method of solving simultaneous equations. Let's use the substitution method.
From the second equation, we can express x in terms of y:
x = 300 - y
Substitute this value of x into the first equation:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = 800 - 1200
-2y = -400
y = -400 / -2
y = 200
Now substitute the value of y back into the second equation 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.
To solve this problem, we need to set up a system of equations.
Let's assume the number of hot dogs sold is represented by 'x' and the number of pretzels sold is represented by 'y'.
According to the given information, the total number of hot dogs and pretzels in stock is 300, so our first equation is:
x + y = 300
The revenue earned from selling hot dogs and pretzels can be calculated by multiplying the number of each item sold by their respective prices. The income goal is $800, so our second equation is:
4x + 2y = 800
Now we have a system of two equations:
x + y = 300
4x + 2y = 800
We can solve this system using various methods such as substitution or elimination.
Let's solve it using the substitution method:
From the first equation, we can solve for x:
x = 300 - y
Substituting this value of x into the second equation, we get:
4(300 - y) + 2y = 800
Expanding and simplifying this equation:
1200 - 4y + 2y = 800
Combining like terms:
-2y = -400
Dividing by -2:
y = 200
Substituting this value of y back into the first 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 in income.
So the correct answer is: 100 hot dogs and 200 pretzels.