A farmer sends his son to market with $100 and tells him to spend the $100 to buy one hundred animals, a mix of chickens, pigs, and cows. Cows cost $10 each, pigs are $3 each, and chickens are $0.50 each. How many of each kind did the boy buy?

Maybe I have got the details mixed up somewhat, but that’s the general trend of it.

I worked it out in my head as I drove home; there is some sort of small mental trick that occured to me that made it simple. What I have forgotten.

This was my response to, and reflection on, what I think Pseudocontext means. It’s a slightly different take than Dan’s, though not quite as succinct.

http://wp.me/pWZ4o-2Z

The question, why the difference in percentage can easily be explained by the fact that you clearly went to different stores; something students have analog experience with.

I agree with Dave as well. To get someone to properly think about the problems, you basically would have to tell them “forget the unicorns and the cubits,” “forget that it’s a lightpole,” or “forget why the taxes are different.” It’s like, though the context isn’t patently false, it still somehow obscures the underlying math. In order to understand the problems, the context needs to be stripped away. In a “good” applications problem, it seems, the math derives naturally from the context.

I don’t know if this has been addressed before, but I think that if we’re trying to get students to agree with us that math describes the world, we should be wary of giving them problems that require a leap of faith or willful suspension of disbelief if we can help it. (“Tomas and Troy come across a water hose and turn it on. Instead of spraying each other, they decide to do math with it.” Get real Mr. Wolf, they’d say. By the way, the water hose “problem” has already been done so much better on this blog, it’s almost not even fair to pick on it.)

All this to say, at some point in my career I’ve given a problem like every last one of these to my kids, and even though I can’t articulate it for all of them, I am starting to see why I won’t anymore (except of course, when they show up in EOC review packets…)

Different city or different state. Tax rates are not uniform around the country. The big problem with the question was that it is not clear whether the “dinner bill” includes tax or not (usually they do) nor whether it includes service charges or not. So the question suffers mainly from vagueness, not from pseudocontext.

A more realistic version of the question would be something like: You have a $35 charge on your credit card for a business dinner which you want to be reimbursed on, but you are not allowed to be reimbursed for alcohol and you had a $3 beer with the dinner. Compute how much you are allowed to be reimbursed, given that the sales tax is 9.25% and you tip 15%. (The tax and tip attributable to the alcohol purchase are also not reimbursable.)