Question

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

Answer 1

Given:

The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2.

To find:

The combined variation equation and find y when x = 6 and z= 3.

Solution:

The variable y varies directly as x and inversely as z.

$y\propto \dfrac{x}{z}$

$y=k\dfrac{x}{z}$           ...(i)

Where, k is the constant of proportionality.

Putting x=4, y=2 and z=14, we get

$2=k\dfrac{4}{14}$

$2=k\dfrac{2}{7}$

$2\times \dfrac{7}{2}=k\dfrac{2}{7}\times \dfrac{7}{2}$

$7=k$

Putting k=7 in (i), we get

$y=7\dfrac{x}{z}$

Putting x=6 and z=3, we get

$y=7\times \dfrac{6}{3}$

$y=7\times 2$

$y=14$

Therefore, the required equation is $y=7\dfrac{x}{z}$ and the value of y is 14 when x = 6 and z= 3.