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
200 hot dogs and 100 pretzels
200 hot dogs and 100 pretzels - no response given
250 hot dogs and 50 pretzels
250 hot dogs and 50 pretzels - no response given
50 hot dogs and 250 pretzels
50 hot dogs and 250 pretzels - no response given
100 hot dogs and 200 pretzels
show you work
To reach the goal of $800, we can set up the following equation:
4*(number of hot dogs) + 2*(number of pretzels) = 800
We also know that the total number of hot dogs and pretzels is 300:
number of hot dogs + number of pretzels = 300
Now we can solve these equations simultaneously:
From the second equation, we can express the number of hot dogs in terms of the number of pretzels:
number of hot dogs = 300 - number of pretzels
Substitute this into the first equation:
4(300 - number of pretzels) + 2(number of pretzels) = 800
1200 - 4(number of pretzels) + 2(number of pretzels) = 800
1200 - 2(number of pretzels) = 800
-2(number of pretzels) = -400
number of pretzels = 200
Substitute the number of pretzels back into the equation for the number of hot dogs:
number of hot dogs = 300 - 200
number of hot dogs = 100
Therefore, the boosters need to sell 100 hot dogs and 200 pretzels to reach their goal of $800.