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12 Percent of Something
12 Percent of Something
"New Brattlebrew has 12% more fruit juice" said the advertisement. No futher explanation was forthcoming from the ad. I asked myself what it meant.
 
We have the old bottle right here on the table, left by our neighbor Ralph who drinks the stuff. Though most of the label is gone we have the words "10% fruit juice" and "extracts of papaya and mango...." and "California redemption value" and nothing else.
 
One interpretation of 12% more, since it once had 10%, is that it now has 22% fruit juice. That would be 12 more percent; not the exact same wording, but ad writers are not mathematicians and cannot be held to precise standards of expression. Of course, the change from 10% to 22% is a 220% increase of the original 10% so marketing would probably have used the larger number. Come to think of it, the increase itself was 120% of the original amount of juice. In this interpretation the ad could have said that there was either a 120% or a 220% increase, depending on how we interpret the ad.
 
I wondered, is the increase by weight or by volume? I didn't know of Brattlebrew were water or alcohol based, but it made a difference. Fruit juice is more dense than water and considerably more dense than alchohol. An increase by weight is a smaller increase than an increase by volume. To see this consider a mix that is half juice and half alchohol by volume (pretend that the liquids don't mix without stirring, so that one is floating on top of the other. I use a cubical box in my mind). The bottom of the volume is half juice. Now consider a mix that is half juice and half alchohol by weight; because the juice is heavier there need be less of it to equal the weight of the alchohol. The mix will be less than half juice. So you get less juice by volume, but the ad didn't say by what measure the "12% more" was calculated.
 
What they were probably trying to say is that the brew has 12% more than the original amount of juice. In other words, they had increased the juice by 12% of the 10%, or that they had gone from 10% to 11.2%. In this interpretation they had added a paltry 1.2% (of the total amount of brew) of juice. If they meant that the amount of juice now in the drink used to be 12% less, then we can calculate backwards and ask of what amount 10 is 88% of. In this case, if there used to be 10%, then there is now 11.36% fruit juice.
 
So far we have 120%, 220%, 1.2% and 1.36% as potential meanings, along with 12%. And each of these has a different interpretation depending on whether the percentages were figured by weight or volume. And it doesn't take much work to get other numbers as well.
 
But they might mean that it has 12% more than its competitor, Brewski, which is only 1% fruit juice to begin with.
 
I have never understood what 12% more meant.
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