# Functions in word problems (§2.6)

If you're asked to find one quantity A as a function of some other quantity x, then you should set up a system of equations with one more variable than equations. You won't be able to solve this completely and find out what A is definitively, but that's OK; all that you need to do is to solve for A in an equation that still has x in it. The general strategy is to solve any equation with x in it for any variable other than x itself and then substitute that solution into the other equations. Eventually, this should leave you with an equation with only A and x in it; when you solve that equation for A, then you're done.

This is all much clearer with examples, and while there are some examples in the textbook, they may make the whole thing seem harder than it has to be. The textbook generally makes do with as few equations and variables as possible, which has the advantage of keeping the thing short, but at the disadvantage of making each equation hard to find. So I've done an example where there are many equations and many variables but each individual equation is very simple and easy to think of. (This used to be an example in the textbook, but they took it out.) Check out the video:

Or download it: WebM format, Ogg Vorbis format, MPEG-4 format.

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