Question

If $z$ varies inversely as w and $z = 20$ when $w = 0.5$, how do you find $z$ when $w = 30$?

Answer 1

Hint:The given question is related to the concept of rational equations and functions. We are given that z is inversely proportional to w. So, we will use the constant k which will represent the directly proportionality and act as a proportionality constant. We are already given values of w and z, from there we will find the value of k. Then, use that vale of k for finding out the value of z when $w = 30$.

Complete step by step answer:
Given is z is inversely proportional to w and $z = 20$ when $w = 0.5$. According to the question, we have z being inversely proportional to w. So,
$z \sim \dfrac{1}{w}$
The symbol ($ \sim $) represents proportionality. We remove this symbol and use the proportionality constant k, which will give us
$z = \dfrac{k}{w}$----(i)
Now, we are given that $z = 20$ when $w = 0.5$. Using these given values in equation (i), we get,
$20 = \dfrac{k}{{0.5}} \\
\Rightarrow 20 \times 0.5 = k \\
\Rightarrow 10 = k$
So, now we have the value of k. Using that along with $w = 30$ in equation (i), we have
$z = \dfrac{{10}}{{30}} \\
\therefore z = \dfrac{1}{3} \\ $
Therefore, the value of z when $w = 30$ is $\dfrac{1}{3}$.

Note:The given question was an easy one. We just made use of arithmetic operations of multiplication and division. Students should not get confused when it is given in the question that a variable is directly or inversely proportional to the other variable. We used the ($ \sim $) symbol to represent proportionality, we could also use the half infinity symbol to represent proportionality. Both of these symbols represent the same.