Question

If $y$ varies jointly as $x$ and $z$ and $y=60$ when $x=3$ and $z=4$, find $y$ when $x$ is $6$ and $z$ is $8.$

Answer 1

Find the relation of $x,y,z$.

$y$ varies jointly as $x$ and $z$

$y=kxz$

Replace $y=60,x=3,z=4$ as shown:

$$\begin{gathered} 60=k\times 3\times 4 \\ \Rightarrow 60=12k \\ \Rightarrow k=\frac{60}{12} \\ \therefore k=5 \end{gathered}$$

Now, determine $y$ when $x=6,z=8$, as shown:

$$\begin{gathered} y=kxz \\ \Rightarrow y=5\times 6\times 8\text{(Substitute 6 for x and 8 for z)} \\ \therefore y=240 \end{gathered}$$

Hence, the value of $y$ is $240.$