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
50 hot dogs and 250 pretzels
50 hot dogs and 250 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
To reach their goal of $800, let's assume they sell x hot dogs and y pretzels.
From the given information, we know that the price of each hot dog is $4 and the price of each pretzel is $2.
Therefore, the total income from selling hot dogs would be 4x and the total income from selling pretzels would be 2y.
To reach the income goal of $800, we can set up the following equation:
4x + 2y = 800
Now we need to find the values of x and y that satisfy this equation.
From the given information, we also know that there are 300 hot dogs and pretzels in stock. In other words, x + y = 300.
We can solve this system of equations using substitution or elimination:
Let's use substitution:
From the equation x + y = 300, we can express x as 300 - y.
Substituting this value of x in the first equation, we get:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Now, substitute the value of y back in x + y = 300:
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.
To reach their goal of $800, we can set up the following equation based on the number of hot dogs (H) and pretzels (P) they plan to sell:
4H + 2P = 800
Since they have a total of 300 hot dogs and pretzels in stock, we can also set up the equation:
H + P = 300
Now we can solve this system of equations to find the values of H and P.
By subtracting the second equation from the first, we have:
(4H + 2P) - (H + P) = 800 - 300
3H + P = 500
Now we can substitute the value of P from the second equation into the third equation:
3H + (300 - H) = 500
3H + 300 - H = 500
2H = 200
H = 100
Substituting this value back into the second equation, we can find the value of P:
100 + P = 300
P = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
To find out 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 based on the given information.
Let's assume the number of hot dogs sold is represented by 'x' and the number of pretzels sold is represented by 'y'.
Based on the given information:
The selling price of each hot dog is $4, so the total revenue from hot dogs sold would be 4x.
The selling price of each pretzel is $2, so the total revenue from pretzels sold would be 2y.
We know that the desired income is $800, so we can set up the equation:
4x + 2y = 800
Additionally, we know that there are a total of 300 hot dogs and pretzels in stock. So we can set up another equation:
x + y = 300
Now we can solve this system of equations to find the values of 'x' and 'y'.
Multiplying the second equation by 2, we get:
2x + 2y = 600
Now we can subtract this equation from the first equation:
(4x + 2y) - (2x + 2y) = 800 - 600
This simplifies to:
2x = 200
Dividing by 2 on both sides, we find:
x = 100
Substituting this value of x into the second equation, we get:
100 + y = 300
Subtracting 100 from both sides, we find:
y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.