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

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

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

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

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

200 hot dogs and 100 pretzels

GPT-4o mini · Answer

Let $ h $ be the number of hot dogs sold and $ p $ be the number of pretzels sold. We have the following two equations based on the problem: 1. The total number of hot dogs and pretzels sold should equal 300: $$ h + p = 300 $$ 2. The total income from selling hot dogs and pretzels should equal $800: $$ 4h + 2p = 800 $$ We can simplify the second equation by dividing everything by 2: $$ 2h + p = 400 $$ Now we have the system of equations: 1. $ h + p = 300 $ 2. $ 2h + p = 400 $ We can subtract the first equation from the second: $$ (2h + p) - (h + p) = 400 - 300 $$ This simplifies to: $$ h = 100 $$ Now, substitute $ h = 100 $ back into the first equation to find $ p $: $$ 100 + p = 300 $$ $$ p = 300 - 100 = 200 $$ So, the boosters need to sell **100 hot dogs** and **200 pretzels**. The correct response is: **100 hot dogs and 200 pretzels**.