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?
Responses
100 hot dogs and 200 pretzels
100 hot dogs and 200 pretzels - not selected, this is the correct answer
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels - incorrect
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels - no response given
250 hot dogs and 50 pretzels
To reach their goal of $800, the boosters need to sell 100 hot dogs ($4 each) and 200 pretzels ($2 each).
So, the correct answer is 100 hot dogs and 200 pretzels.
give step by step
Sure! Here's the step-by-step solution:
1. Let's start by figuring out the total income that can be earned by selling each item:
- Hot dogs: $4 each
- Pretzels: $2 each
2. The boosters want to earn $800 in total.
Let x be the number of hot dogs sold and y be the number of pretzels sold.
Based on the information given, we can create the following equations:
- 4x (income from selling hot dogs) + 2y (income from selling pretzels) = 800
- x + y = 300 (total number of hot dogs and pretzels available in stock)
3. We can solve the system of equations using substitution or elimination method. From the second equation, we have:
x = 300 - y
Now substitute x = 300 - y into the first equation:
4(300 - y) + 2y = 800
1200 - 4y + 2y = 800
-2y = -400
y = 200
4. Substitute y = 200 back into x = 300 - y to find x:
x = 300 - 200
x = 100
5. Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.