Question

Write an equation describing the relationship of the given variables. y varies jointly as x, z and w. When x=2, z=1 and w=12, then y=72. Find y when x=1, z=2 and w=3.The value for y is:Answer

Answer 1

Given:

There are given that the y varies jointly as x, z, and w.

And,

The value of x, z, w, and y are:

$\begin{gathered} x=2 \\ z=1 \\ w=12 \\ y=72 \end{gathered}$

Explanation:

According to the above statement, the initial statement is:

$y\propto xzw$

Then,

To convert the equation by multiplying k:

$\begin{gathered} y\propto xzw \\ y=kxzw\ldots(1) \end{gathered}$

Then,

Put the value of x, y, z, and w into the above equation to find the value of k.

So,

From the equation (1):

$\begin{gathered} y=kxzw \\ 72=k(2)(1)(12) \\ 72=k(24) \\ k=\frac{72}{24} \\ k=3 \end{gathered}$

Then,

Put the value of k into the equation (1):

So,

$\begin{gathered} y=kxzw \\ y=3xzw\ldots(2) \end{gathered}$

Now,

Put,

$x=1,z=2,w=3$

Into the equation (2) to find the value of y.

So,

from the equation (2):

$\begin{gathered} y=3\text{xzw} \\ y=3(1)(2)(3) \\ y=3(6) \\ y=18 \end{gathered}$

Final answer:

Hence, the value of y is 18.