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 po int)

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 po int)
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

GPT-4o mini · Answer

Let $ x $ be the number of hot dogs sold, and $ y $ be the number of pretzels sold. We have the following two equations based on the problem: 1. The total number of items sold (hot dogs and pretzels) must equal 300: $$ x + y = 300 $$ 2. The total income from selling hot dogs and pretzels must equal $800: $$ 4x + 2y = 800 $$ Now, we will solve this system of equations. From the first equation, we can express $ y $ in terms of $ x $: $$ y = 300 - x $$ Now, substitute this expression for $ y $ into the second equation: $$ 4x + 2(300 - x) = 800 $$ Distributing the 2: $$ 4x + 600 - 2x = 800 $$ Combining like terms: $$ 2x + 600 = 800 $$ Subtract 600 from both sides: $$ 2x = 200 $$ Dividing both sides by 2 gives: $$ x = 100 $$ Now, substitute $ x = 100 $ back into the equation for $ y $: $$ y = 300 - 100 = 200 $$ Thus, the Baynard High School Boosters need to sell **100 hot dogs and 200 pretzels** to reach their goal of $800. The answer is: **100 hot dogs and 200 pretzels**