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 $800? say you had 300 of x and 300 of y and you needed to get 800 dollars from both x and y, if they sold x for 4$ and y for 2$ how many of of x and y do they need to sell

Answer 1

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.