​Yesterday, a movie theater sold 266 bags of popcorn. A large bag of popcorn costs ​$3. A small bag of popcorn costs ​$1. In​ all, the movie theater made ​$458 from popcorn sales.

Question

Write and solve a system of equations to find how many bags of each size of popcorn were sold.

Answer 1

Hi Nicole!

We can think of the number of each size of popcorn as an unknown variable. So let's just use b for big and s for small.

So, b is the number of big bags sold. So we can say b + s = 266. That is the number of small bags plus big bags sold is equal to 266 bags in total.

How can we compare the number of bags of each size to the total profits? Well how much would one big bag of popcorn cost? Two? Three? The pattern here is the multiple of $3. That is the cost of a bag times the number of bags. So we can say 3b + 1s = 458.

Now we have two equations and two unknowns (b and s) which means we can solve this system of equations. How would we do this? There are two ways, but I think the easiest would be to set these two equations equal to each other. So s = 458 - 3b = 266 - b.

Now we just have the unknown b that we can solve for. That's the total number of big bags sold. Now what about the s? Well once you have b, you can just plug that number into any of the two equations and you'll be able to find s.

I hope that helps! Let me know if you have any other questions.