Question

Z varies directly with x and inversely with y.

When x = 6 and y = 2, z = 15.
What is the value of z when x = 4 and y = 9?

Answer 1

z =
`(20)/(9)`

Explanation:

Given that z varies directly with x and inversely with y then the equation relating them is

z =
`(kx)/(y)` ← k is the constant of variation

To find k use the condition when x = 6 and y = 2, z = 15, thus

15 =
`(6k)/(2)` ( multiply both sides by 2 )

30 = 6k ( divide both sides by 6 )

5 = k

z =
`(6x)/(y)` ← equation of variation

When x = 4 and y = 9, then

z =
`(5(4))/(9)` =
`(20)/(9)`