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?

Question

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?

Answer 1

Let x be the number of hot dogs and y be the number of pretzels. We have the following system of linear equations:

x + y = 300 (the total items to sell)

4x + 2y = 800 (the total income they want to earn)

We can solve the system by substitution or elimination.

Using substitution, we can solve the first equation for x:

x = 300 - y

Now, substitute this expression for x in the second equation:

4(300 - y) + 2y = 800

Distribute the 4:

1200 - 4y + 2y = 800

Combine like terms:

-2y = -400

Divide by -2:

y = 200

Now, we can find the number of hot dogs:

x = 300 - y
x = 300 - 200
x = 100

So, they need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.