"There were some people on a train. 19 people get off the train at the first stop. 17 people get on the train. Now there are 63 people on the train. How many people were on the train to begin with?"
Someone posted up this math-quiz type problem, noting that most six and seven year old kids were not able to comprehend the questions, the formula, or the output.
If you had thrown this question up around the fifth or sixth grade with the kids I was associated with....I would imagine three would have been able to come to the answer.
At least two kids would have asked where this train started from, the location of the first stop, and where it ended. I probably would have been one of the two kids myself.
At least one kid would have asked who was counting the seventeen people who got on, and if they could have screwed up.
At least one kid would have asked who the heck travels by train....of which the entire class would have noted that they don't know anyone who has ever traveled by train unless they were over the age of sixty-five.
One bright kid from the class would have asked from the 19 people getting off and 17 people getting on....is it possible that one of the 19 simply stepped off to relieve themselves, and got right back on after finishing their business (thus being one of the 17). In this case, 'X' could vary.
Along about the seventh-grade of my life....I came to a woeful period in math with 'word-problems'. A four-line problem would represent a ten-minute reading, analysis, and would force me into asking what is the real question at hand. The red-herring dilemma would be the best description of this situation. At some point, I just started making 'X' into twelve as I started the problem, and as I came to the end....I would note the difference between 12 and the wrong answer....thus making a stupid but workable method of handling word-problems.
I can make the observation of life today....that the majority of people (minimum of fifty-percent) over the age of twenty....can't handle word-problems. It's simply that their mind isn't geared to that type of analysis and output. I'd also make the observation that 10-percent of society are geared toward world-problems, and routinely do these dozens of times per days with ease. These are the people who note the size of a bale of hay, the dimensions of a wagon, and casually note that only 75 bales can fit safely upon the wagon.
In some ways, I think society is wasting its time trying to get 100-percent of people to work with X and Y type word-problems. Some folks were destined to become rocket-scientists.....and some weren't. In this train episode.....does anyone really care that nineteen folks got off the train?