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 100 hot dogs and 200 pretzels 100 hot dogs and 200 pretzels 250 hot dogs and 50 pretzels 250 hot dogs and 50 pretzels 50 hot dogs and 250 pretzels 50 hot dogs and 250 pretzels 200 hot dogs and 100 pretzels
Let's assume the boosters sell x hot dogs.
They will earn 4x dollars from selling hot dogs.
They plan to sell 300 hot dogs and pretzels in total, so they will have 300 − x pretzels left to sell.
They will earn 2(300 − x) = 600 − 2x dollars from selling pretzels.
To reach their goal of $800, the total income from selling hot dogs and pretzels must be 800 dollars: 4x + 600 − 2x = 800.
Combining like terms, we get 2x + 600 = 800.
Subtracting 600 from both sides gives 2x = 200.
Dividing both sides by 2 gives x = 100.
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal. Answer: \boxed{100 \text{ hot dogs and } 200 \text{ pretzels}}.
To figure out how many hot dogs and pretzels the boosters need to sell, we can set up a system of equations.
Let x be the number of hot dogs sold and y be the number of pretzels sold.
According to the information given, the boosters want to earn an income of $800.
From selling hot dogs: 4x
From selling pretzels: 2y
So, the total income should be 4x + 2y.
We also know that there are 300 hot dogs and pretzels in stock. Therefore, the number of hot dogs and pretzels sold, x + y, should be equal to 300.
So we have the following equations:
4x + 2y = 800
x + y = 300
Solving this system of equations will give us the values of x and y.
Multiplying the second equation by 2, we get:
2x + 2y = 600
Subtracting this equation from the first equation, we have:
(4x + 2y) - (2x + 2y) = 800 - 600
2x = 200
x = 100
Substituting the value of x in the second equation, we find:
100 + y = 300
y = 200
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
Hence, the correct response is:
100 hot dogs and 200 pretzels.
To solve this problem, we need to set up an equation based on the given information.
Let's assume that the boosters sell x number of hot dogs and y number of pretzels.
The income generated from selling hot dogs can be calculated as 4 * x.
Similarly, the income generated from selling pretzels can be calculated as 2 * y.
According to the given information, the total income required is $800.
So, we can set up the equation as follows: 4x + 2y = 800.
Now, to find the number of hot dogs and pretzels the boosters need to sell, we need to solve this equation.
Unfortunately, you have provided some duplicate answer options. However, among the unique options, we can see that the equation 4x + 2y = 800 can be satisfied by either option: 200 hot dogs and 100 pretzels or 250 hot dogs and 50 pretzels.
So, the correct answer is either:
- 200 hot dogs and 100 pretzels, or
- 250 hot dogs and 50 pretzels.