Question

Given that r is directly proportional to

y and inversely proportional to Z,
x= 15 when y = 10 and Z= 4, find
the equation connecting x, y and Z.​

Answer 1

Given:

x is directly proportional to y and inversely proportional to z.

x= 15 when y = 10 and z= 4.

To find:

The equation that connecting x, y and z.​

Solution:

It is given that, x is directly proportional to y and inversely proportional to z.

`x\propto (y)/(z)`

`x=(ky)/(z)` ...(i)

Where, k is the constant of proportionality.

We have, x= 15 when y = 10 and z= 4.

`15=(k(10))/(4)`

`15* 4=10k`

`60=10k`

Divide both sides by 10.

`(60)/(10)=k`

`6=k`

Putting k=6 in (i), we get

`x=(6y)/(z)`

Therefore, the required equation is
`x=(6y)/(z)`.