Question

A concession stand sells two sizes of popcorn. The small bag holds 20 ounces and costs $4, and the large bag holds 32 ounces and sells for $6. The concession stand sold 200 bags of popcorn and made $900 from the sale of popcorn.

Answer 1

Before you read: Hello! My name is Matthew and I will be doing the elimination method. If you don't know what that is; follow the steps I provide! I will show you step by step how to solve this problem. Okay! You may continue with the answer! :)

Answer:

Large bags of popcorn sold = 50

Small bags = 150

Explanation:

Our two equations are:

s(small bags) + L(large bags) = 200(number of bags sold)

4s + 6L = $900(how much money was made)

Let's multiply the first equation by -4 to cancel our s value when we add the equations together.

-4s + -4L = -800.

Our equations now look like this:

First equation: -4s + -4L = -800

Second equation: 4s + 6L = 900

Add the two equations together,

2L = 100

Divide by two,

L = 50.

Now that we know our L value, we can go back way up to the first sentence and substitute 50 for L. Our equation now looks like this:

s + 50 = 200.

Subtract 50 from each side of the equals,

s + (50 - 50) = (200 - 50)

Our equation now looks like this:

s = 150.

Our final answer: 150 small bags of popcorn sold, and 50 large bags.

Thank you for reading my response. If this has helped, leave a thank you! It would be really appreciated and would show me if you learned something from this! Have a good day and stay safe! BTW, this answer is right on Edmentum.

Answer 2

x = large bag of popcorn
y = small bag of popcorn

x + y = 200...x = 200 - y
4x + 6y = 900

4(200 - y) + 6y = 900
800 - 4y + 6y = 900
-4y + 6y = 900 - 800
2y = 100
y = 50 <=== large bags sold

x + y = 200
x + 50 = 200
x = 200 - 50
x = 150 <== small bags