Question

An inverse variation includes the points (10, 2) and (n, 4). Find n.

Answer 1

An inverse variation is given as

`\begin{gathered} a\text{ }\propto\text{ }(1)/(b) \\ \text{Introducing a constant k, we have } \\ a\text{ = }(k)/(b) \end{gathered}`

Putting a = 10 and b = 2, we have;

`\begin{gathered} 10\text{ = }(k)/(2) \\ k\text{ = 10 x 2 = 20 } \end{gathered}`

The relationship becomes

`\begin{gathered} a\text{ = }(20)/(b) \\ \text{Putting a = n, and b = 4, we have } \\ n\text{ = }(20)/(4) \\ \\ n\text{ = 5} \end{gathered}`

Therefore, n = 5