Question

If x varies inversely as y and x=16 when y=5, find x when y=20.

Answer 1

Since x varies inversely as y, then it can be represented as the expression below:

`y=(1)/(a)\cdot x`

Where a is the proportionality constant. We need to find a to determine the value of x when y is 20. For that we will use the two values given as shown below:

`\begin{gathered} 5=(1)/(a)\cdot16 \\ 5\cdot a=16 \\ a=(16)/(5)=3.2 \end{gathered}`

The expression is:

`y=(1)/(3.2)\cdot x`

If y is 20, then x must be:

`\begin{gathered} 20=(1)/(3.2)\cdot x \\ x=3.2\cdot20 \\ x=64 \end{gathered}`

The value of x must be 64.