How To Solve Variation Problems

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Since 4 are absent, that leaves 8 workers (12 – 4 = 8).

We can thus solve the problem as detailed below: The correct answer is 9 hours.

Problems involving direct variation can be solved using proportions.

Let’s see this in action: If it takes 3 gallons of paint to cover 100 square feet, how many gallons of paint will be needed to cover 600 square feet?

Let’s take a look at an example of direct variation.

The amount of flour needed in a bread recipe varies with the number of loaves being made.Making more loaves will require more flour; making fewer loaves will require less flour.In direct variation, the variables (amount of flour and number of loaves in our example) will move in the same direction.Let’s take a look at an example: Note, in the above example, you could have also solved this problem by observation if you recognized that 4/12 is simply 1/3. Observations such as this will provide significant time savings on the exam, but on more difficult problems, it’s important to know the basics.Variations deal with explaining, in mathematical language, how one quantity changes with respect to one or more other quantities.Joint variation is just an extension of direct variation.When we say that " is 8) into our joint variation equation: Once we have a value forwe plug this back into the equation of joint variation along with the variables we do know and solve for our unknown: Combined variation involves both direct and inverse variation. (Note, we are using different letters for our variables, but it doesn’t matter! The steps are the same as in the other example problems.The constant of variation, , is simply 6 • 12 = 72.We want to know the numbers of hours it will take the remaining custodians to do the job.In this example, the time required to paint the house varies inversely with the number of people painting.This means the more people painting the house, the less total time it will take to paint.


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