Question

Suppose that y varies jointly with w and x and inversely with z and y = 320 when w = 6, x = 20, and z = 3.

Answer 1

Answer:

The joint variation says that:

$y \propto x$ and $y \propto \frac{1}{z}$

then equation is in the form of:

$y = k\frac{x}{z}$ where, k is the constant of variation.

As per the statement:

As y varies jointly with w and x and inversely with z

By definition joint variation we have;

$y = k\frac{wx}{z}$, .....[1]   where k is the constant of variation.

Given: y = 320 when w = 6 , x = 20 and z = 3

Solve for k

Substitute these in [1] we have;

$320 = k\frac{6(20)}{3}$

⇒$320 = k \cdot 2 \cdot 20$

⇒$320 = 40k$

Divide both sides by 40 we have;

$8 = k$

or

$k = 8$

Then the constant of variation is. 8 and the equation of variation is,

$y =8 \cdot \frac{wx}{z}$

Answer 2

I suppose we are to determine the proportionality constant of the variation. The equation for this proportionality is,
                          y = kwx / z
Substituting the known values,
                            320 = k(6)(20)/3
The value of k from the equation is 8.