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)
A. 100 hot dogs and 200 pretzels
B. 200 hot dogs and 100 pretzels
C. 50 hot dogs and 250 pretzels
D. 250 hot dogs and 50 pretzels
Let's assume the boosters sell x hot dogs and y pretzels.
The income earned from selling hot dogs is 4x dollars.
The income earned from selling pretzels is 2y dollars.
We can set up the following equation:
4x + 2y = 800.
Since we have a total of 300 hot dogs and pretzels in stock, we know that x + y = 300.
Solving these two equations simultaneously, we can find the values of x and y.
Subtracting 4y from both sides of the first equation gives:
4x = 800 - 2y.
Dividing both sides by 4 gives:
x = (800 - 2y)/4.
Substituting this value of x into the second equation:
(800 - 2y)/4 + y = 300.
Multiplying both sides by 4 gives:
800 - 2y + 4y = 1200.
Simplifying:
2y = 400.
Dividing both sides by 2 gives:
y = 200.
Substituting this value of y into the second equation:
x + 200 = 300.
Simplifying:
x = 100.
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels.
The answer is A. 100 hot dogs and 200 pretzels.
Let's use a step-by-step approach to find the answer.
First, let's determine the income earned from selling hot dogs. They plan to sell the hot dogs for $4 each, and they have 300 in stock. So the income from selling hot dogs can be calculated as follows:
Income from selling hot dogs = Number of hot dogs x Price per hot dog
Income from selling hot dogs = 300 x $4
Income from selling hot dogs = $1200
Next, let's determine the income earned from selling pretzels. They plan to sell the pretzels for $2 each, and they have 300 in stock. So the income from selling pretzels can be calculated as follows:
Income from selling pretzels = Number of pretzels x Price per pretzel
Income from selling pretzels = 300 x $2
Income from selling pretzels = $600
Now, let's add the income from selling hot dogs and the income from selling pretzels to find the total income earned:
Total income earned = Income from selling hot dogs + Income from selling pretzels
Total income earned = $1200 + $600
Total income earned = $1800
Since the boosters want to earn an income of $800, the correct option is:
D. 250 hot dogs and 50 pretzels
To solve this problem, we need to set up two equations based on the given information.
Let's assume the number of hot dogs the boosters sell is "x" and the number of pretzels they sell is "y".
According to the information given, the boosters have a total of 300 hot dogs and pretzels in stock. Therefore, we can write our first equation as:
x + y = 300 --------------- (equation 1)
Now, let's consider the prices of the hot dogs and pretzels. Each hot dog is sold for $4, and each pretzel is sold for $2. To reach their income goal of $800, the boosters need to earn $800 by selling hot dogs and pretzels. Therefore, our second equation becomes:
4x + 2y = 800 --------------- (equation 2)
Now we can solve the system of equations.
We can multiply equation 1 by 2, which gives us:
2x + 2y = 600
We can now subtract this equation from equation 2:
(4x + 2y) - (2x + 2y) = 800 - 600
2x = 200
x = 100
Substituting the value of x back into equation 1, we get:
100 + y = 300
y = 200
Therefore, the booster needs to sell 100 hot dogs (option A) and 200 pretzels (option A) to reach their goal of $800.