Question

If $y$ varies directly with $x$ and $y=12$ when $x=0.5$, then what is $y$ when $x=3$?

Answer 1

Step-1: Find relation between $y$ and $x$:

It is given that $y$ varies directly with $x$.

$$\begin{gathered} \Rightarrow y\propto x \\ \Rightarrow y=kx\dots \left(1\right) \end{gathered}$$

where $k$ is constant of proportionality.

Step-2: Find value of constant $k$.

According to the question, $y=12$ when $x=0.5$.

Substituting $x=0.5$ and $y=12$ in equation $\left(1\right)$, we have

$$\begin{gathered} \Rightarrow 12=k\left(0.5\right) \\ \Rightarrow \frac{12}{0.5}=k\left[\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}\left(0.5\right)\right] \\ \therefore k=24 \end{gathered}$$

Step-3: Find $y$ when $x=3$.

Substituting $x=3$ and $k=24$ in equation $\left(1\right)$, we have

$$\begin{gathered} \Rightarrow y=24\left(3\right) \\ \therefore y=72 \end{gathered}$$

Hence, value of $y$ is $72$.