Solving the Right Problem Right

Presh Talwalkar recently wrote a blog post about people trying to solve problems with no solution.

I want to add something to this.

The numbers in a real world problem have meaning. You can not just do arithmetic operations without regard for what the numbers mean and expect to get a correct answer except by fluke.

Mathematical tools have requirements for their use. For example, if one has two of voltage, current, and resistance for some types of electrical circuits, one can compute the third using the formula E=IR. BUT you must have two of the values. If you only have one of them, you do not have enough information.

In a real world problem, you may have to hunt down the missing information. Sometimes, you can compute a missing value from other information given in the problem.

For example, in the problem “Albert has 25 marbles more than Carl does. Beth has 45 marbles. Carl has 15 fewer marbles than Beth. How many marbles does Albert have?”, Albert has c + 25 marbles. We do not know the value of c, but we do know that c = b – 15. That still is not enough, but since we know b = 45, we can substitute 45 for b to get c = 45 – 15 = 30 and then for c in a = c + 25 to get a = 30 + 25 = 55. Thus, Albert has 55 marbles.

Note that it was necessary to do something else before c could be computed. This is not a trick question. It is simply that one must have the necessary pieces before one can proceed.

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