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)

Question

Responses

100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels

200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels

250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels

50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels

Answer 1

To reach their goal of $800, the boosters need to sell a combination of hot dogs and pretzels that adds up to $800.

Let h = number of hot dogs sold
Let p = number of pretzels sold

The total income earned will be: 4h + 2p

We are given:
h + p = 300
4h + 2p = 800

Solving these two equations simultaneously:
h + p = 300
4h + 2p = 800

Multiply the first equation by 2:
2h + 2p = 600

Subtract the first equation multiplied by 2 from the second equation:
(4h + 2p) - (2h + 2p) = 800 - 600
2h = 200
h = 100

Now that we have the number of hot dogs sold, we can find the number of pretzels sold by substituting h back into the first equation:
100 + p = 300
p = 200

Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.

Correct response:
100 hot dogs and 200 pretzels