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)

Question

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

Answer 1

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.