All posts by davidg

Blending Whisky – A New Project for College Algebra and Finite Math

Now that the Spring semester is over, I have been working on a number of new projects. You might wonder why I would ever need to update projects…the answer is simple. Not only do I have students who repeat my courses for one reason or another, but I have also learned that over time a number of technical memos for my projects are publically available. By changing the projects (especially those for the beginning of the semester), I keep them fresh for me and defeat attempts by my students to not do their own work.

The Blending Whisky Project is designed to replace two projects I have used for several semesters. In the Gas Prices Project and the Arsenic Removal From Drinking Water Project, students set up a system of two equations in three variables. Typically, they use matrices to solve the system of equations and then analyze the resulting solutions similar to what is described in the Dependent System Handout ( The Blending Whisky Projects utilizes the exact same type of solution strategy, but with mixing Scotch Whisky from several different casks at a distillery.

For this project, students read a little backgound material on Scotch Whisky ( before reading the letter which gives the problem statement ( This introduces them to the concept of alcohol by volume (concentration) and some of the unusual terms used to describe the casks in Scotland.

Like the other projects, students must come up with an equation for the total volume in the Scotch Whisky blend (the easy equation) and another for the total amount of alcohol in the Scotch Whisky blend (the challenging equation). The system has many solutions and using the information on cask sizes, they can come up with a range of acceptable solutions. I have also included a long list ( of commercially available cask strength Scotch Whiskies with prices you might use. Most of the prices are for a 70 centiliter bottle.

I plan to use this project in the Fall semester for my online and face-to-face Finite Math classes. This topic area is very rich for math applications. While researching this project, I came up with information for two other projects. The prices mentioned above might be used to create a linear programming project. The evaporation of alcohol and water from the aging casks can be used to come up with a function modeling the alcohol by volume as a function of time. The model can be a ratio of linear functions or a ratio of exponential functions and leads to some great graphs. Look for these new projects in the next few weeks. If you have any questions or corrections, feel free to comment or drop me an email at dave at symbol

Welcome to the New PBL Pathways!

For the last several years PBL Pathways has been a fairly static website…a few new projects each semester, a couple posts about conferences I attended, ect. For the future, I am going to use this blog style entry page in an attempt to be more dynamic.

A number of users have requested more details on how I run my classes, how I come up with new projects, and other similar information. Next semester (starting in August) I’ll document what is going on in my classrooms (I’ll be finished with my sabbatical year) and what I am doing to update projects.

You’ll still find all of the pages you are used to on this site…they can be accessed through the navigation links across the top. Some of the pages maybe spruced up a bit, but they are basically the same.

I’ll caregorize my blog posts so you can find the information on the blog easier…I’ll have a Projects category to hightlight new and existing projects, and categories for each of the classes I teach, College Algebra, Finite Math, and Survey of Calculus. I may add more categories as the need arises.