I see these problems all the time when I'm tutoring, and I'm always surprised by how similar they are between teachers, schools and textbooks. And so plug-and-chuggable! So, in the videos below, I'll show you an iron-clad series of steps that will solve these problems every time, because all these problems are basically the same.
Direct & Inverse Variation: Two Variables
These two types of problems always involve two letters (usually x and y) and usually start the same way: if the problem has the words "varies directly" in it (or says two things are "proportional"), you just write down "y=kx" and start plug-and-chugging. If the problem says "varies inversely" (or variables are "inversely proportional"), you write down y=k/x and start plug-and-chugging. Sound too easy? What can I say: the same four steps will get you through every one of these things.
Joint Variation: Three or More Variables
These problems are exactly like the problems in the previous video, except instead of 2 variables there are three or four. Either way, same series of steps! "Directly" will still mean multiply, and "inversely" will still mean divide, and "plug and chug" will still be in your future. CAUTION: this video won't make a ton of sense unless you watch the one before it, so I'd recommend that first.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)