Question

If x varies inversely with y and x = 4 when y = 8, find x when y = 16. 32 8 2 4

Answer 1

x = 2

Explanation:

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

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

To find k use the condition x = 4 when y = 8

k = xy = 4 × 8 = 32, hence

x =
`(32)/(y)` ← equation of variation

When y = 16, then

x =
`(32)/(16)` = 2

Answer 2

Answer: 2 (third option)

Explanation:

The equation of inverse variation where the variable "x" varies inversely as the variable "y", has the form:

`x=(k)/(y)`

Where "k" is the constant of variation.

As you know that
`x=4` when
`y=8`, then you can substitute values and solve for the constant of variation "k":

`4=(k)/(8)\\\\k=4*8\\k=32`

Substitute "k" and
`y=16` into
`x=(k)/(y)` to find x when
`y=16`:

`x=(32)/(16)\\\\x=2`