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?
250 hot dogs and 50 pretzels 250 hot dogs and 50 pretzels 200 hot dogs and 100 pretzels 200 hot dogs and 100 pretzels 50 hot dogs and 250 pretzels 50 hot dogs and 250 pretzels 100 hot dogs and 200 pretzels
To reach their goal of $800, the Boosters need to sell x hot dogs and y pretzels, where x represents the number of hot dogs and y represents the number of pretzels.
The total income from selling hot dogs can be represented as 4x, and the total income from selling pretzels can be represented as 2y.
Since they want to earn a total of $800, we can write the equation as:
4x + 2y = 800
We also know that they have 300 items in stock, so:
x + y = 300
To solve these equations simultaneously, we can use substitution or elimination. Here, we will use substitution:
First, solve the second equation for y:
y = 300 - x
Now substitute this into the first equation:
4x + 2(300 - x) = 800
4x + 600 - 2x = 800
2x = 200
x = 100
Now that we have found x, we can find the number of pretzels by substituting back into y = 300 - x:
y = 300 - 100
y = 200
Therefore, the Boosters need to sell 100 hot dogs and 200 pretzels to reach their income goal of $800.