The variable y varies directly as x and inversely as z. When x = 4 and z= 14, y=2. Write a combined variation equation and find y when x = 6 and z= 3.

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.

          ...(i)

Where, k is the constant of proportionality.

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

Putting k=7 in (i), we get

Putting x=6 and z=3, we get

Therefore, the required equation is and the value of y is 14 when x = 6 and z= 3.