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
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels
250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels
To solve this problem, we need to set up a system of equations. Let's say x represents the number of hot dogs sold and y represents the number of pretzels sold.
The first equation represents the total income earned from hot dogs:
4x
The second equation represents the total income earned from pretzels:
2y
The total income earned is $800, so we can set up the equation:
4x + 2y = 800
We also know that the boosters have 300 hot dogs and pretzels combined in stock, so we can set up another equation:
x + y = 300
Now we can solve the system of equations.
Let's use the substitution method. Solve the second equation for x:
x = 300 - y
Substitute this value of x into the first equation:
4(300 - y) + 2y = 800
Distribute and simplify:
1200 - 4y + 2y = 800
-2y = -400
y = 200
Now substitute this value of y 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 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 use the variables "h" for the number of hot dogs and "p" for the number of pretzels.
The boosters plan to sell the hot dogs for $4 each, so the total revenue from selling hot dogs will be 4h. Similarly, the pretzels will be sold for $2 each, resulting in a total revenue of 2p.
Therefore, we can set up the following equation:
4h + 2p = 800
We also know that the boosters have a total of 300 hot dogs and pretzels in stock:
h + p = 300
Now, we can solve this system of equations to find the values of h and p.
Using the second equation, we can rewrite it as h = 300 - p.
Substituting this expression for h into the first equation, we have:
4(300 - p) + 2p = 800
Simplifying the equation, we get:
1200 - 4p + 2p = 800
Combining like terms, we have:
-2p = -400
Dividing both sides by -2, we get:
p = 200
Substituting this value back into the equation h = 300 - p, we have:
h = 300 - 200 = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800. Hence, the correct answer is:
100 hot dogs and 200 pretzels.