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:

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.

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.

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 Studio, Teaching 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! http://bit.ly/O8TwN5 |

### Angela Culley

#### Latest posts by Angela Culley (see all)

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Thanks for stopping by Megan!

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!

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

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

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.

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: http://nobleandpond.blogspot.com/2014/04/come-along-wednesdays-2.html

Thanks for stopping by Jean!

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.