Question

Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

Answer 1

`x = -36`

Explanation:

The basic inverse variation equation is

`xy = k`

where `k` is the constant of variation. In order to write the equation that reflects this relationship, we must find `k`. We use the known relationship of `x = 12` and `y = 9` to find `k`. Substituting in the basic equation, we will find `k`:

`xy = k`

`(12)(9) = k`

`108 = k`

This then yields the equation which relates `x` and `y`:

`xy = 108`

Now, use this equation and substitute the second value of `y` in order to find its related value of `x`:

`xy = 108`

`x(-3) = 108`

`x = 108/(-3)`

`x = -36`