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)
200 hot dogs and 100 pretzels
50 hot dogs and 250 pretzels
250 hot dogs and 50 pretzels
100 hot dogs and 200 pretzels
Let h be the number of hot dogs and p be the number of pretzels. We know that h + p = 300 and 4h + 2p = 800.
From the first equation, we can solve for h: h = 300 - p.
Substituting this into the second equation, we get: 4(300-p) + 2p = 800.
Simplifying the second equation, we get: 1200 - 4p + 2p = 800.
Combining like terms, we get: -2p = -400.
Dividing both sides by -2, we get: p = 200.
Substituting this back into the first equation, we get: h + 200 = 300.
Subtracting 200 from both sides, we get: h = 100.
Thus, the Baynard High School Boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800. Answer: 100 hot dogs and 200 pretzels.
Let's assume the boosters sell x hot dogs and y pretzels.
According to the given information, they plan to sell hot dogs for $4 each and pretzels for $2 each.
Therefore, the total income from selling hot dogs would be 4x and the total income from selling pretzels would be 2y.
The total income they want to earn is $800, so we can create the following equation:
4x + 2y = 800
Now let's consider the number of hot dogs and pretzels in stock. The boosters have 300 hot dogs and pretzels in total.
Therefore, we can create the second equation:
x + y = 300
We can solve this system of equations to find the values of x and y.
Using substitution or elimination method, we can solve the system of equations:
x + y = 300 ----(1)
4x + 2y = 800 ----(2)
Multiplying equation (1) by 2, we get:
2x + 2y = 600 ----(3)
Subtracting equation (3) from equation (2):
4x + 2y - (2x + 2y) = 800 - 600
2x = 200
Dividing by 2:
x = 100
Substituting the value of x into equation (1):
100 + y = 300
y = 300 - 100
y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
The correct answer is:
100 hot dogs and 200 pretzels
To determine the number of hot dogs and pretzels the boosters need to sell, we can set up a system of equations.
Let's assume x represents the number of hot dogs sold and y represents the number of pretzels sold.
From the given information, we know that each hot dog sold generates $4 in revenue, and each pretzel sold generates $2 in revenue. The boosters need to earn a total of $800 in revenue.
Therefore, we can set up the following equations:
4x + 2y = 800 (equation 1)
x + y = 300 (equation 2)
Now, we can solve the system of equations to find the values of x and y.
One way to solve this system is by substitution. We can solve equation 2 for x in terms of y and substitute it into equation 1. Let's do that:
x = 300 - y (equation 3)
Substituting equation 3 into equation 1:
4(300 - y) + 2y = 800
Simplifying:
1200 - 4y + 2y = 800
-2y = 800 - 1200
-2y = -400
y = -400 / -2
y = 200
Now that we have the value for y, we can substitute it back into equation 2 to find x:
x + 200 = 300
x = 300 - 200
x = 100
Thus, 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.