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? (1 point)
Let x be the number of hot dogs and y be the number of pretzels sold.
The income from selling hot dogs is 4x and the income from selling pretzels is 2y. The total income is the sum of these two amounts:
4x + 2y = 800
The number of hot dogs and pretzels sold must also add up to the total number in stock:
x + y = 300
We can solve these two equations simultaneously. First, we can solve the second equation for x:
x = 300 - y
Now, we can substitute this expression for x into the first equation:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
Now that we have found the number of pretzels sold, we can find the number of hot dogs sold by substituting this value back into the equation x = 300 - y:
x = 300 - 200
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.