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.