## Wednesday, March 2, 2011

### Slyly shifting sizes and prices, Part II

My wife likes Sun Free & Clear clothes detergent. It has no dyes and no smells. Today I set out to buy some.

According to the Sun website, my choices are 45, 78 and 117 ounces. But the package I bought in the store says 188 ounces, and it offered me 8 extra bonus loads of wash compared to the 112 load package. Did I get the largest package? And the best price?

To quote Excel Math's own inimitable Bob Parrish, "It is impossible to say at this time." They don't tell me on the website and don't even mention the enormous bottle that I bought. It looks like  we need some elementary mathematics, as taught in our Excel Math curriculum.

Let's make a table and see what we find:

45  = a
78   = b
117 = c
x   = 112
188 = 120

188 ounces ÷ 120 loads = roughly 1.56 ounces per load. Using this figure, we can calculate the missing values for a, b, c and x.

45  = 29
78   = 50
117 = 75
175 = 112
188 = 120

The scented versions of Sun come in even more sizes. Here they are

62  = 40
150 = 96

Here's the whole line-up.

45  = 29
62  = 40
78  = 50
117 = 75
150 = 96
175 = 112
188 = 120

Is this reminding you of the Hershey bar exercise yesterday?  Now we need to know exactly what we are buying - is it ounces or loads? And how much might it cost per load or ounce?

"It is impossible to say at this time."

I looked around on the web and found a price from Amazon for the 45 ounce / 29 load bottles of Sun Free & Clear. If I buy 6 bottles the site says they would cost \$54.83 "retail" or 29.34 from them. That last price is only 11¢ per ounce. Or I could get a "subscription" and have it delivered every month and save 15%. Now that complicates things further.

Price per wash load can be calculated in various ways. Here are some possibilities:

Retail  (54.83 ÷ 6) = \$9.14 per bottle ÷ 29 loads =  31.5¢ per load
Actual ((29.24 ÷ (6 x 29)) = \$29.24 ÷ 174 =  16.8¢ per load
Subscription  24.94 ÷ 6 = \$4.16 per bottle ÷ 29 loads =  14.3¢ per load

In fact I did not buy my Sun on the Internet, I bought it at Big Lots and paid a better price. How much better?  Is it impossible to say at this time?  No, it is possible to say.

My price was \$6.00 ÷ 120 loads = 5¢ per load or 3.2¢ per ounce

PS - the price for the 175 ounce / 112 load bottle was also \$6.00. So I did get 8 bonus loads as promised on the bottle. So who would buy the smaller bottle for the same price? It is impossible to say at this time.