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)
Responses
200 hot dogs and 100 pretzels
100 hot dogs and 200 pretzels
250 hot dogs and 50 pretzels
50 hot dogs and 250 pretzels
To solve this problem, we can set up a system of equations. Let's say the boosters sell x hot dogs and y pretzels.
The income from selling hotdogs is 4x, and the income from selling pretzels is 2y. The total income should be $800, so we can write the equation:
4x + 2y = 800
We also know that the boosters have 300 hot dogs and pretzels in stock, so the total number of items sold should be x + y = 300.
To solve this system of equations, we can use substitution or elimination.
Let's use substitution. Solve the second equation for x: x = 300 - y.
Substitute this expression for x in the first equation:
4(300 - y) + 2y = 800
Distribute and simplify:
1200 - 4y + 2y = 800
Combine like terms:
-2y = 800 - 1200
-2y = -400
Divide by -2:
y = 200
Now substitute this value for y in the second equation:
x + 200 = 300
Subtract 200 from both sides:
x = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.
So the answer is 100 hot dogs and 200 pretzels.