Let x be the number of hot dogs and y be the number of pretzels. We have:
x + y = 300 (since they have 300 hot dogs and pretzels in stock)
4x + 2y = 800 (since they want to earn $800 from selling hot dogs and pretzels)
To solve this system of equations, we can use the substitution method. We can solve the first equation for y:
y = 300 - x
Now, substitute this expression for y in the second equation:
4x + 2(300 - x) = 800
Simplify and solve for x:
4x + 600 - 2x = 800
2x = 200
x = 100
Now that we have the value of x, use it to find the value of y:
y = 300 - 100
y = 200
So the boosters must sell 100 hot dogs (x) and 200 pretzels (y) to reach their goal of $800.