Joint Variation

What is Joint Variation?

Joint Variation refers to a scenario in which the value of one variable depends on two, or more, other variables when the other variables are held constant. For example, one may say, "C varies jointly as A and B, if C=ABX for some constant X." Once understood, the concept can be used to represent the interactions of multiple variables at once.

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How does Joint Variation work?

While the concept can be challenging to conceptualize with variables, it is often helpful to incorporate an example. For example, if C is jointly proportional to A and B and C=6, when A=3 and B=4, find C when A=7 and B=4. First, we must begin by finding our constant variable, referred to above as X. If we know that C=6, when A=3 and B=4, the formula is 6=3(4)X. Thus, we can deduce that the value for X is .5. Now, we can plug our X value back into the new equation as C=7(4)(.5). This means that the value of C, when A=7 and B=4 is 14.