We have some of these mini cans of ginger ale in the house this week. I am not sure where they came from; only that my wife bought them. Normally we only have sparkling water around, not pop (nor soda, nor…)
So I’m looking at the can instead of grading like I should be and I notice the “25% fewer calories than regular ginger ales” claim.
And I think what any skeptical consumer ought to think. Sure fewer calories in the mini can. Duh.
Then I see this:
They have controlled for the size of the can. Nice. This one has 60 calories per 7.5 fl. oz. Regular ginger ales have 90 calories per 7.5 fl. oz.
I am briefly satisfied. And impressed.
But wait! 60 is 25% less than 90? ARGH!
Two possible explanations:
- 25% means at least 25%, and Seagram’s chose this nice simple number over the more complicated .
- It really is exactly 25%. But we know that calorie counts are rounded to the nearest 10 calories.
This second explanation leads to a sort of lovely task. How can we characterize the set of possible calorie counts for 7.5 fl. oz. of Seagram’s and of regular ginger ale so that, (a) the counts round to 60 and 90, and (b) one number is exactly 25% less than the other?
Extra credit: Which standards for mathematical practice are you using as you solve?
Double extra credit: Which of my abbreviated list of standards for mathematical practice (see below) are you using as you solve? And which was I using as I gazed at my can of ginger ale?
Prof. Triangleman’s Abbreviated List of Standards for Mathematical Practice.
PTALSMP 1: Ask questions. Ask why. Ask how. Ask whether your answer is right. Ask whether it makes sense. Ask what assumptions you have made, and whether an alternate set of assumptions might be warranted. Ask what if. Ask what if not.
PTALSMP 2: Play. See what happens if you carry out the computation you have in mind, even if you are not sure it’s the right one. See what happens if you do it the other way around. Try to think like someone else would think. Tweak and see what happens.
PLALSMP 3: Argue. Say why you think you are right. Say why you might be wrong. Try to understand how someone else sees things, and say why you think their perspective may be valid. Do not accept what others say is so, but listen carefully to it so that you can decide whether it is.
See also my Desmos graph of this relationship.