Question

If z varies directly with x and inversely with y, when x = 2, y = 5, and z = 10, what is z when x = 3 and y = 15?

Answer 1

Given:

z varies directly with x and inversely with y, when x = 2, y = 5, and z = 10.

To find:

The value of z when x=3 and y=15.

Solution:

It is given that z varies directly with x and inversely with y. So,

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

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

Where k is the constant of proportionality.

We have x = 2, y = 5, and z = 10. After substituting these values, we get

`10=k\cdot (2)/(5)`

`10* 5=2k`

`(50)/(2)=k`

`25=k`

The value of k is 25. After substituting k=25 in (i), we get

`z=25\cdot (x)/(y)` ...(ii)

We need to find the value of z when x=3 and y=15. Substituting x=3 and y=15 in (ii), we get

`z=25\cdot (3)/(15)`

`z=25\cdot (1)/(5)`

`z=5`

Therefore, the value of z is 5 when x = 3 and y = 15.