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Chapter 7: Problem 45

In your own words, explain how to solve a variation problem.

Short Answer

Expert verified
Variation problems involve identifying the type of variation (direct, inverse, or joint), writing an appropriate equation to model the relationship, substituting known values into the equation, and then solving for the unknown. These problems require knowledge of math and algebra and may involve additional steps to find the constant of variation.

Step by step solution

01

Identifying the Type of Variation

Differentiate between direct, inverse, and joint variation. In direct variation, as one quantity increases, the other also increases (or as one decreases, the other also decreases). In inverse variation, as one quantity increases, the other decreases. In joint variation, one quantity varies with respect to more than one other quantity.
02

Write the Variation Equation

For direct variation: the equation is \(y=kx\), where \(k\) is the constant of variation. For inverse variation: the equation is \(y=k/x\) or \(xy= k\), where \(k\) is the constant of variation. For joint variation: the equation is \(y=kxz\), where \(k\) is the constant of variation and \(x\) and \(z\) are different quantities.
03

Substitute Known Values into the Equation

Replace the variables in the equation with the actual figures. If there's a quantity you don't know yet, retain the variable. Remember that some variation problems may require mathematical manipulation, such as reversing the terms first before substitution.
04

Solve the Equation

Using your basic knowledge of math and algebra, find the unknown variable. Be sure to answer in the right measurement unit. Also, if the problem requires additional steps, such as finding the constant of variation, perform these as well.

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