## Thursday, February 21, 2013

### Systems of Linear Equations - Help with Applications

I have this idea in my head.  I want my students to compare two products and tell us which one to buy and why.  I would like to model the end product that I'm looking for and I'll use soda stream as my example.  The big question will be "Should I buy the soda stream or continue to drink name brand soda products?"  I will consider things like cost, convenience, the environment, quality, etc.  The big math part of this will be writing two linear equations (one for each product), making a table, and graphing the equations, to determine which is the better price at varying levels.

But that's where I'm stuck.  I want to create a list of products for my students to choose from, but I'm not coming up with a lot of ideas.  Help!!

My thoughts so far:

K-cups vs. regular brewing.  (I'm thinking the lines for this would not intersect in the 1st quadrant.)
Dishwasher vs. hand-washing?????

1. Here is one I use - I have them compare the plans of two different cell phone providers and select the provider that is the best fit for their personal needs (cost, minutes, data paln, etc) and then tell me which they would select based on the mathematics of the situation.

another I have used is along the same idea but with a security system to install in my home. I select 2, one with no installation fee, and one with an installation fee.

2. Compare laundry machine vs. laundromat

3. Anything you might buy individually at a grocery store vs. buying it in bulk at a wholesale store like Sam's Club or BJ's. Students could decide if it's worth it to pay for the membership to the wholesale store.

4. How about an annual pass to an amusement park vs buying single day tickets.

5. How about a membership to something like a gym or golf club. For instance I get a year membership at my local golf course for \$1000 but I can play for \$32 a round instead. This could generate some good discussion. For instance if I have the membership I could care less if it rains three holes in but i sure wasted money if I bought an individual round of golf. So would I play more if I have the membership... Lots of good real life questions, maybe not tied into your system of equations though(although the actual comparison would be)

6. Traditional pencils vs mechanical pencils? Problem is coming up with an average time that each lasts. You could also use furniture rental versus buying furniture with a situation of living somewhere for a limited amount of time.