Additional Math Pages & Resources

Thursday, March 3, 2011

Slyly shifting sizes and prices, Part III

This is the third post on how prices can be moved up and down while the contents of the package are also moving. We looked at Hershey Bars, Sun Clothes Detergent and today we'll consider paper towels. The "adjustments" that manufacturers make with towels are not too difficult for elementary mathematicians to figure out.

There are lots of kinds of paper towels - the ones you find wadded up near a sink at a public restroom, and the ones in your kitchen are the most common. I think I'll concentrate on the kitchen and leave the janitor alone today. By the way, the packaging and pricing of toilet paper is very similar to paper towels.


As seen in the photo above on the left, most paper towels fit onto a holder that stands on the counter or hangs from a cabinet. We have the hanging kind and have discovered that today's new "extra large double" rolls don't fit. (Same applies to the toilet paper!)

Here are the variables in paper:

Layers = single-ply, double-ply, triple-ply
Texture = plain, quilted, soft, abrasive, woven, perforated
Size = full (sort of square 11" x 11"), rectangular
Paper = white (bleached), brown (unbleached), new, recycled
Length of Roll or Roll Size = who knows!

Here are some packages I found:
  • 1 roll x 90 sheets x 1-ply
  • 15 rolls x 103 sheets x 2-ply
  • 24 rolls x 88 half-sheets x 2-ply
  • 24 mega-rolls x 102 sheets x 2-ply
  • 30 rolls x 51 sheets x 2-ply 
  • 1 roll x 80 sheets (11" x 9") x 2-ply quilted 60% recycled
  • 1 roll x 120 sheets (10" x 8") x 2-ply 100% recycled; 80% post-consumer
  • 30 rolls x  85 sheets x 2-ply 95% recycled; 10% post-consumer
  • 6 rolls x 140 sheets x 2-ply 100% recycled; 60% post-consumer recycled
While shopping on Amazon for paper towels I realized that another eager math-lover had done a great deal of this comparison work for me. If you want to see his analysis, you can click here.

If you want to see what a group of statisticians do when given a 4 cases of towels, read on. I have just extracted one small test. There are 14 more pages of this stuff in the actual report. Which you can easily download here. But I wouldn't advise it. Yawn.

If you just want to know which are the best towels to buy for drying your hands or wiping up a mess, sorry. I have just one piece of advice for you:

It is impossible to say at this time.