Question

If y varies inversely as x and y = 12 when x = 3, how do you find y when x = 4?

Answer 1

`y=9` when `x=4`

Explanation:

If `y` varies inversely as `x` then
`color(white)("XXX")color(blue)(x) * color(red)(y)=c` for some constant `c`

Given `y=color(red)(12)` when `x=color(blue)(3)`
`color(white)("XXX")color(blue)(3) * color(red)(12) = c`

`color(white)("XXX")rArr c=36`

So
`color(white)("XXX")x * y = 36`
and when `x=color(green)(4)`
`color(white)("XXX")color(green)(4) * y = 36`

`color(white)("XXX")rArr y=9`