Question

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.

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 (x)/(z)`

`y=k(x)/(z)` ...(i)

Where, k is the constant of proportionality.

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

`2=k(4)/(14)`

`2=k(2)/(7)`

`2* (7)/(2)=k(2)/(7)* (7)/(2)`

`7=k`

Putting k=7 in (i), we get

`y=7(x)/(z)`

Putting x=6 and z=3, we get

`y=7* (6)/(3)`

`y=7* 2`

`y=14`

Therefore, the required equation is
`y=7(x)/(z)` and the value of y is 14 when x = 6 and z= 3.