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Maths II

Variation

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# Inverse Variation

In an inverse variation (proportion), the values of the two variables change in an opposite manner - as one value increases, the other decreases.

Inverse proportion is described in the language of variation as follows -

• varies inversely as
• is inversely proportional to
• (read as varies inversely as )
• , where is the constant of variation

For example, the number of days required to build a bridge varies inversely to the number of workers. As the number of workers increases, the number of days required to build would decrease.

## Example

varies inversely as , and when .

• (a) Find a formula connecting and
• (b) Determine when
• (c) Determine when

## Solution

(a)

(b) Find the value of : , so

Using the formula, and constant , find the missing value of when :

(c)

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