Word problems

Understanding word problems is probably the most important part of mathematics. Mathematics without applications (‘pure’ mathematics) is a beautiful work of art, part of our global culture, and good practice for precise thinking. But only applied mathematics is directly useful.

Almost everything in Algebra can be taught to a computer, and while it's good to know how computer algebra systems work, in the end it's more reliable to use them to solve problems than to solve them yourself, just as your calculator is more likely to do 276,435/6,250 correctly than you are, no matter how good you are at arithmetic. But word problems cannot be taught to a computer, and without word problems, Algebra is ultimately useless.

The reason that we can't teach word problems to a computer is that there is no way to make the principles behind them fully precise. This means that I also have no way to teach them to you perfectly. However, I can give you some advice:

If you just cannot find a single quantity x that every other quantity can be written with, then you may need to use more than one variable, in which case you also need to find more than one equation. This is the topic of Chapter 4, which we'll get to later on. In general, if you can find as many equations as variables, then you can make it work.

If you just cannot find a quantity with two different expressions, or more generally if you can't find as many equations as you have variables, then there might not be enough information to solve the problem. If you can find at least two different ways to simultaneously assign values to all of the quantities that makes the entire story make sense, then you know that this is the case! But there shouldn't be any trick questions like that in the assignments in this class.


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