Okay, I'm back. Thanks for your responses.
First, let me say my intention here was not to make anyone feel stupid, but to point out that something is seriously wrong with the way we teach math (and other subjects as well, I'm guessing). And I say this is a teacher.
First, a few confessions.
I'm sure many of you already suspsected this was not a real situation (some of you asked when are tile and carpet ever the same price, and wouldn't different styles of carpet and tile have different pricing. All very good "real-world" thinking). It wasn't. It was one of those "word" problems in my freshman Algebra assignment yesterday. The reason I posed it as a "real situation" was because if I'd said, "hey, can anyone solve this word problem" people might have said. . "Who cares. I hate word problems!" (That's what I would have said anyway).
Second confession. I wouldn't have been able to tell whether my "sister" had been cheated either. My students had questions on that problem when we were grading their homework yesterday, and we all worked on it together. Eventually we solved it, but we had two advantages you didn't. I had the teachers edition with the answer, so we were able to think "how did they get this answer" rather than "what is the answer AND how did they get it." Second advantage is that the students knew what this Algebra unit was about (solving systems) so they had a clue as to what they might need to do to solve the problem.
The solution, by the way is this:
Yes, she was lied to. The regular cost of the carpet, paid by the "friend" and "the boss" was $16 per square yard, the cost of the tiles (it was linoleum in the textbook, but I figured someone would ask 'who buys linoleum anymore?') was $4 per square yard. With those prices, a 10% discount should have been $9000, not $9600. She got a discount but not as much as she was told.
Don't feel bad that you got it wrong. I'm very doubtful I'd have gotten it right if I hadn't had those two advantages. And even with them I'm not sure I'd have gotten it right if I hadn't been teaching Algebra for the past five years.
So now for the FYM issue: The problem, I'm suggesting, is not that we're not "that smart". I consider the people on this thread (for the most part
pretty intelligent, perhaps more intelligent than average. The problem is in the way that we teach math.
What struck me is that this situation sounded close enough to real life that it could actually happen, and I realized most of us wouldn't know if we were being misled. My students and I started talking about this yesterday and that's when we decided to post this, to "test our theory."
I guess my point is that, I hate word problems as much as the next person, but I think this is what we really need to be teaching. "Word problems." Real-life situations with real life variables using the tools of mathematics to solve them. Our schools do not teach problem solving. . .of any kind. And if we do, it's an afterthought---a couple of "word problems" at the end of 20 "exercises" to complete. And I think this is to all of our detriment.
You know you'll hear students complain about how they have to "learn all this crap we'll never use" and, in a sense, they're right.
what do you think?
Oh, and by the way those that are annoyed at me for "messing with you", I can deal with that. I deserve it