The Roots of the Equation

No Right Answer

A bit ago I got yelled at by a commenter on Kate’s blog who claimed that being always right is why we like math. The problem with that point of view is that, while yes, you can always be right while doing computation, math isn’t just computation. So the other day I was talking with a friend of mine, and that prompted me to post the following tweets:

My friend Phil (@albrecht_letao) responded to the question, and he came up with an answer of $20/hr. When I worked it out with my friend, we came up with $14.25. Does that mean one of us is wrong, since we got different numbers?

No, of course not. What happened is we approached the problems in different ways. Phil only calculated the monetary value: with his amount, my friend would earn the same amount of money she does now. He figured this was an important way to look at it, for paying bills and whatnot. Our calculation came from thinking about how her time is being compensated. Since those 16 hours are being wasted (she has to work them for free; actually, she pays to lose that time), we calculated her “real” hourly rate and used that.

There can be more answers than even these two, depending on what you think is important. But it’s a clear example of a problem, solved using math, with no one right answer. That’s what math is about. I tweeted it thinking maybe it could be a problem worth considering in class, to show that essential idea to students.

What do you think?

P.S. The right answer, of course, came from @calcdave: