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?
Responses
200 hot dogs and 100 pretzels
50 hot dogs and 250 pretzels
100 hot dogs and 200 pretzels
250 hot dogs and 50 pretzels
The correct answer is: 100 hot dogs and 200 pretzels.
To find this answer, we can set up a system of equations:
Let x represent the number of hot dogs sold.
Let y represent the number of pretzels sold.
From the given information, we know the following:
x + y = 300 (the total number of hot dogs and pretzels)
4x + 2y = 800 (the total income needed)
Solving this system of equations, we can find the values of x and y. By substituting x = 300 - y into the second equation, we have:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substituting y = 200 into the first equation, we have:
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 the number of hot dogs and pretzels the boosters need to sell to reach their income goal of $800, we can set up a system of equations. Let's use the variables "h" for the number of hot dogs and "p" for the number of pretzels.
Since the boosters plan to sell the hot dogs for $4 each, the income from hot dogs can be calculated as 4h. Similarly, the income from pretzels can be calculated as 2p, since pretzels are sold for $2 each.
We are given that the boosters want to earn a total income of $800 from selling both hot dogs and pretzels. Therefore, we can set up the equation 4h + 2p = 800.
Additionally, we know that they have a total of 300 hot dogs and pretzels in stock. So we can set up another equation: h + p = 300.
Now we have a system of equations:
4h + 2p = 800
h + p = 300
We can solve this system of equations to find the values of h and p.
The correct answer is 250 hot dogs and 50 pretzels.
To determine the number of hot dogs and pretzels the boosters need to sell to reach their goal of $800, we can set up an equation based on the cost of each item.
Let's say the number of hot dogs sold is represented by 'x' and the number of pretzels sold is represented by 'y'.
The cost of each hot dog is $4, so the revenue generated from selling hot dogs would be 4x.
Similarly, the cost of each pretzel is $2, so the revenue generated from selling pretzels would be 2y.
Since the total revenue needed is $800, we can set up the equation:
4x + 2y = 800
Now, we need to consider the number of hot dogs and pretzels in stock. Given that there are 300 hot dogs and pretzels in stock, we can add the constraint:
x + y = 300
Solving these two equations simultaneously will give us the values of 'x' and 'y', representing the number of hot dogs and pretzels needed to reach the goal.
Let's solve them using the elimination method:
From the second equation, we can rewrite it as x = 300 - y.
Substituting this value into the first equation:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Substituting the value of y back into the second equation:
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