## Tuesday, October 18, 2011

### The math of re-tiring?

Today in the math blog I would like to consider some math related to re-tiring. What do I mean? Is it:
• retire - stop performing one's work or withdraw from one's position
• retire - back away, retreat
• retire - go to bed
• retire - take out of circulation or recall (as in paper currency, bonds, etc)
• retire - strike out or throw out (in baseball)
• re-tire - put new tires on your car
I am interested only in the last of these definitions - changing the tires on your car, motorcycle or bicycle. If you've had to replace tires recently, you know it can be complicated. This is not like buying a pound of potatoes! Let's look at the pieces of the puzzle.

TIRES

I researched types, sizes and prices on all sorts of tires this morning. Here's what I found:

 Type of tires Low Price High Price Low Weight High Weight Car & Light Truck 49 742 16.0 86.0 Motorcycle & Scooter 34 384 8.0 23.0 Bicycle & Unicycle 12 140 0.3 2.8

Although these are all tires, it's apparent that we cannot compare them directly. Even within each category, the range is tremendous. I divided the weight by the dollars and came up with this:

 Type of tires Low cost per pound High cost per pound Car & Light Truck \$0.57 \$46 Motorcycle & Scooter \$1.48 \$48 Bicycle & Unicycle \$4.26 \$467

This is not way to choose which tires to buy. The "value per unit" is not found by comparing the  weights! Tire prices are not related to how much rubber you get. In fact, with bicycles, it's the other way around - the price is related to how little weight you get.

The best way to choose a tire is to read reviews on national tire websites and then talk to the manager of your local tire, motorcycle or bicycle store.

INSTALLATION

Tires are a nuisance to install. You lift the vehicle, take off the wheel, leave a corner of the vehicle lifted (or motorcycle/bicycle on a stand). Using a tool or machine, you remove the tire from the wheel, put the new one on, inflate the tire, and reinstall it on the vehicle. Very few of us can do this work at home - we must rely on the expertise of a mechanic. In a former job I changed thousands of bicycle tires. I can appreciate the labor involved!

 Type of Tires Installation Cost Car & Light Truck \$5-25 Motorcycle & Scooter \$10-175 Bicycle & Unicycle \$10-30

EXTRAS

As if this wasn't enough, we are faced with a barrage of optional-at-extra-cost services associated with the tires and the replacement. We must think about purchasing:

 Type of Tires Stem or  Tube Align or True Balance HazMat Weights Warranty Car & Light Truck \$3-20 \$30-75 \$12-15 \$5-10 \$3-5 \$10-15 Motorcycle & Scooter \$5-30 \$20-50 \$10-20 \$5 \$3-5 \$50 yr Bicycle & Unicycle \$7-30 \$10-30 0 0 0 0

Without a basic understanding of math, how can we even compare bottom-line prices for tires?

We can't!  Here's a typical formula that shows how your \$100 tire really costs \$151.50.

\$432  Tires \$100 x 4 = \$400 x 1.08 (tax) = \$432
\$  65  Mount & balance \$15 x 4 = 60 x 1.08 = \$65
\$  13  Stems \$3 x 4 = 12 x 1.08 = \$13
\$  16  Disposal fees \$4 x 4 = \$16
\$  80  Road Hazard warranty 4 x \$20 = \$80
\$606  Cost Per tire = \$606 ÷ 4 = \$151.50