Author David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)
Abstract
My Ford Ranger is no more and my students were getting wise to the Gas Prices Project, so I created a similar project using a bit of knowledge supplied by my hydrologist wife. This uses the same basic idea but incorporates blending of drinking water from several sources to result in a system of equations with many solutions.
- Content Area – College Algebra, Finite Math
- Time Frame – 2 to 3 weeks with mini-lectures
- Published – August 15, 2009, updated 3/3/2014
- Keywords – system of Linear Equations, matrices, row echelon form, systems with an infinite number of solutions
Project Content
Project Background (PDF)
Scaffolding Resources
Technology Assignment: Write Out Equations (DOC | PDF) This assignment introduces students to documenting their work with the equation editor in Word.
What is Parts per Million or Parts per Billion? (PDF)
Technology Assignment: Row Operations on the Ti-83 (DOC | PDF)In this assignment, students create their own system of equations and then use row operations to solve the system. This assignment is almost identical to the one above, but this version includes instructions for carrying out the row operations on a TI graphing calculator and documenting the steps using Mathtype. This document has been updated to show how to use the Equation Editor in Word 2007 or 2010 (as well as Mathtype).
Technology Assignment: Write and Solve a System Using Excel (DOC | PDF) This assignment is designed to get students to write down their system of equations for the project so that they can be checked before turning in the final assessment for the project.
Dependent Systems Handout (PDF)
Reduced Row Echelon Form on a TI Graphing Calculator (PDF) This document takes a student through the steps of putting an augmented matrix into a TI calculator and using the rref command to find the reduced row echelon form for the augmented matrix.
Reduced Row Echelon Form in Excel (PDF)This document shows how to do row operations in Excel in order to end up with the reduced row echelon form of an augmented matrix.
Row Operations on the TI-83 (Video)
RREF in Excel (2 equations, 2 variables) (Video)
RREF in Excel (3 equations, 3 variables) (Video)
Notes
- You can drop the number of wells down to 2 to make the problem a bit easier or increase the number of wells. Adding costs for pollution removal (and still blend) could make for an interesting linear programming problem.