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

50 hot dogs and 250 pretzels
50 hot dogs and 250 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

100 hot dogs and 200 pretzels

GPT-4o mini · Answer

Let $ h $ represent the number of hot dogs sold and $ p $ represent the number of pretzels sold. We can set up the following equations based on the problem: 1. The total number of items (hot dogs and pretzels) is 300: $$ h + p = 300 $$ 2. The total income from selling hot dogs and pretzels must be $800: $$ 4h + 2p = 800 $$ Now we can solve these equations step by step. First, let's solve equation (1) for $ p $: $$ p = 300 - h $$ Next, substitute this expression for $ p $ into equation (2): $$ 4h + 2(300 - h) = 800 $$ Expanding the equation gives: $$ 4h + 600 - 2h = 800 $$ Combine like terms: $$ 2h + 600 = 800 $$ Subtract 600 from both sides: $$ 2h = 200 $$ Divide both sides by 2: $$ h = 100 $$ Now use this value of $ h $ to find $ p $: $$ p = 300 - 100 = 200 $$ Thus, the solution is: - Hot dogs: 100 - Pretzels: 200 So, the boosters need to sell **100 hot dogs and 200 pretzels** to reach their goal of $800.