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?
A. 200 hot dogs and 100 pretzels
B. 50 hot dogs and 250 pretzels
C. 100 hot dogs and 200 pretzels
D. 250 hot dogs and 50 pretzels
Let x be the number of hot dogs sold and y be the number of pretzels sold.
We can set up the following equations:
4x + 2y = 800 (total income equation)
x + y = 300 (total quantity equation)
We can solve this system of equations by substitution or elimination.
Let's use elimination to solve the system.
Multiply the second equation by 2 to get: 2x + 2y = 600
Subtract this equation from the first equation to get: (4x + 2y) - (2x + 2y) = 800 - 600
Simplify: 2x = 200
Divide both sides by 2: x = 100
Substitute this value back into the second equation to solve for y: 100 + y = 300
Subtract 100 from both sides: y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800, which matches option C: 100 hot dogs and 200 pretzels.
To figure out how many hot dogs and pretzels the boosters need to sell, we need to set up a system of equations.
Let's assume that the boosters sell x hot dogs and y pretzels.
The income from selling hot dogs can be calculated as 4x, and the income from selling pretzels can be calculated as 2y.
We know that the total income the boosters want to earn is $800, so we have the equation:
4x + 2y = 800
We also know that the boosters have 300 hot dogs and pretzels in stock, so we have the equation:
x + y = 300
Now we can solve these equations to find the values of x and y.
We can start by multiplying the second equation by 2 to make the coefficients of x and y the same:
2(x + y) = 2(300)
2x + 2y = 600
Now we have a system of equations:
4x + 2y = 800
2x + 2y = 600
We can subtract the second equation from the first equation:
(4x + 2y) - (2x + 2y) = 800 - 600
2x = 200
Dividing both sides of the equation by 2, we find:
x = 100
Substituting the value of x = 100 into the second equation, we find:
100 + y = 300
y = 300 - 100
y = 200
So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Therefore, the answer is option C. 100 hot dogs and 200 pretzels.
To solve this problem, we need to set up an equation based on the given information. Let's denote the number of hot dogs as "x" and the number of pretzels as "y".
According to the problem, the total number of hot dogs and pretzels in stock is 300. Therefore, we have the equation:
x + y = 300 (Equation 1)
The income from selling hot dogs can be calculated by multiplying the number of hot dogs sold by the price per hot dog, which is $4. Similarly, the income from pretzels can be calculated by multiplying the number of pretzels sold by the price per pretzel, which is $2. Since the boosters want to earn a total income of $800, we have the equation:
4x + 2y = 800 (Equation 2)
Now, we have a system of equations with two variables (x and y). Solving this system will give us the values for x and y, which represents the number of hot dogs and pretzels the boosters need to sell to reach their goal.
To solve this system of equations, we can use different methods like substitution, elimination, or graphing. Let's use the substitution method:
From Equation 1, we can rewrite x as follows: x = 300 - y
Substituting this value of x into Equation 2, we get:
4(300 - y) + 2y = 800
Expanding and simplifying the equation:
1200 - 4y + 2y = 800
-2y = 800 - 1200
-2y = -400
Dividing both sides by -2:
y = -400 / -2
y = 200
Substituting this value of y back into Equation 1, we can solve for x:
x + 200 = 300
x = 300 - 200
x = 100
So, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Therefore, the correct answer is option C: 100 hot dogs and 200 pretzels.