Re: Rule to Apply for Rates and Ratios

[John Denker <jsd@AV8N.COM>]

Quoting Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>:

> No wonder kids aren't
> learning anything in school - teachers can't formulate
> proper questions!

Maybe that's part of it.........

But one could at least as plausibly argue the opposite point,
that kids are not sufficiently trained to deal with ill-posed
questions.

Real life is *not* a multiple-choice question where one of the
answers is clearly right and the others are clearly wrong.

In real life, almost all questions are ill-posed in one way
or another, perhaps underspecified, perhaps overspecified,
perhaps self-contradictory, et cetera.

In real life, if the boss asks you a question, or if the
customer asks you a question, you are expected to answer the
question even if it is not completely well-posed.

For the trivial example of buying eggs, the rule is simple:
just ANSWER THE QUESTION.  You can answer in terms of eggs
per dollar, or you can answer in terms of dollars per egg.
Usually the preferred form can be inferred from the question,
but if not, just pick one and answer the question.  Indeed
it wouldn't kill you to give both answers!

If the size and grade of egg aren't specified in the question,
you should take your pick and specify it as part of the answer.
Just answer the question already.

For additional discussion and examples, see
  http://www.av8n.com/physics/ill-posed.htm