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These are the questions I am exploring with this month’s real life math problem.

Are refillable mugs worth the cost?

Will they save you money?




As I was filling up my gas tank at a local station, I noticed the following sign:

Real Life Math - Roo Mug Price

I wondered if this was a deal I should take advantage of or would I lose money. I run across deals like the one above all the time at places like gas stations, amusement parks, and coffee shops.

I definitely needed more information before making a decision, so I walked into the store and looked around for the price of a typical fountain drink. I noticed there were several different sizes and prices.

Real Life Math - Drink Prices

The Roo mug appeared to be a 20oz mug, so I decided to compare the cost of the Roo mug to the cost of the 20oz fountain drink.

I immediately thought of using a system of equations to help me determine if this deal would save me money.

If x = the number of cup fills I purchase and y = the total cost,

y = 1x + 1.99 (This equation represents the Roo mug)

y = 1.29x (This equation represents the disposable cup)

I started by graphing each equation and making a comparison.

Real Life Math -Graph Comparison

It looks like like the disposable cup is the better buy if I don’t drink a lot of soda, but if I do stop and buy a soda regularly, the Roo cup might be the better buy.  I wonder how many drinks I would need to purchase before the Roo mug became the better buy? It is hard to tell from the graph, so I’m going to use substitution to find the exact point where these two lines intersect.

1.29x = 1x + 1.99

.29x = 1.99

x = 6.86

It looks like my 1st through 6th disposable cup is cheaper than the Roo mug, but if I plan on buying 7 or more drinks, I am better off buying the Roo mug. Not to mention, I’m sure it is better for the environment.

Are you looking for other ideas about using real life math? Take a few seconds to read the post Math is Real Life – Grocery Shopping Edition. This post will provide you an idea of how math is used to bargain shop at the grocery store.

A monthly REAL WORLD math blog link-up hosted by
4mulaFun, Fourth Grade StudioTeaching to Inspire in 5th, AND MissMathDork.

Click to Tweet: Wondering when you will ever use math in the real world? Check out these examples that will help you save money! 

Angela Culley

Angela Culley

Owner & Tutor at Math Ninja, LLC
As the founder of Math Ninja, Angela provides online and in person math tutoring for all ages including those studying for the GRE, GMAT, SAT, ACT, PPST, and other math specific subject assessments. Prior to launching her business, Angela coached K-12 educators on effective teaching strategies, curriculum writing, and assessment development.As a classroom teacher, she taught math to students ranging from grade 5 - 12. She has also taught both undergraduate and graduate math courses as an adjunct professor at the University of Virginia and Mountain State University.
Angela Culley
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9 thoughts on “Real Life Math – Discount Drinks Edition

  • Pingback: Real Life Math - Strawberry Picking Edition | MATH NINJA

  • April 3, 2014 at 6:45 pm

    Like Megan said, I also struggled with math growing up, so this real-life example is great! I have also wondered if those refillable cups are worthwhile.

    Thanks for answering the question and sharing on Hump Day Happenings!

  • April 3, 2014 at 11:48 am

    Thanks for stopping by Megan and for your kind words. I will definitely stop by your linkup. Thanks for the invite!

  • April 3, 2014 at 11:47 am

    Me too! I was always asking why and looking for real life examples. Thanks for stopping by Jenna.

  • April 2, 2014 at 1:06 pm

    I always wanted “real life” examples like this when I was learning math. I understand it better when I can apply it to something in my life. Thanks for sharing this with Hump Day Happenings.

  • April 2, 2014 at 12:30 pm

    First of all, where have you been all my life? 🙂 I have always struggled with math, and you made it look so easy! Secondly, I am stopping by from Hump Day Happenings at A Savory Feast and The Walker Fireside Chats, and I would love it if you linked up your post with my blog hop as well. You can find it here:

  • March 29, 2014 at 12:50 pm

    I just found your site via the Saturday Sharefest. I love the math is real life concept and will bookmarking this blog to share with my 2 boys.

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