Question

Write an equation describing the relationship of the given variables. y varies jointly as x and z and inversely as w. When x=5, z=2 and w=20, then y=4. Find y when x=3, z=8 and w=48.The value for y is:Answer

Answer 1

Answer:

y varies jointly as x and z and inversely as w. will be represented below as

$\begin{gathered} y\propto\frac{xz}{w} \\ y=\frac{kxz}{w} \end{gathered}$

When x=5 , z=2 and w =20 then y=4

$\begin{gathered} y=\frac{kxz}{w} \\ 4=\frac{k\times5\times2}{20} \\ 4=\frac{10k}{20} \\ \text{cross multiply, } \\ 4\times20=10k \\ 10k=80 \\ \text{divide both sides by 10} \\ \frac{10k}{10}=\frac{80}{10} \\ k=8 \end{gathered}$

The equation connecting x,y,z,w i given below as

$y=\frac{8xz}{w}$

To figure out the value for y,when x=3,z=8 and w=48

$\begin{gathered} y=\frac{8xz}{w} \\ y=\frac{8\times3\times8}{48} \\ y=\frac{192}{48} \\ y=4 \end{gathered}$

Hence,

The value of y= 4