Joint Variation: Combining Constant Ratios AND Constant Products [Deep Dive 03]

In today's video, we'll look at precisely how to combine direct and inverse variation scenarios through joint variation. You can tackle joint variation problems in several ways, and I highlight two of them: setting up a table to keep track of your elements, letting them grow proportionally or inversely as the situation demand. Or setting up an equation using what is essentially a unit rate, then solving for unknowns much like we do in directly proportional relationships.
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One of the keys to approaching these problems is to build a good intuitive sense of what kinds of situations require constant *ratios*. These can be represented as direct variation questions. Both of the quantities exhibit the same relationship, either both increasing or both decreasing. Then you'll want to note scenarios that require constant *products*. These can be represented as inverse variation questions. One quantity grows while the other lessens correspondingly.
Joint variation occurs in scenarios where we have more than just two quantities we're comparing, and we can tell that different pairs of quantities exhibit different relationships when we hold the other constant.
#algebra #inversevariation #jointvariation
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