Question

If y varies inversely as twice x. When x = 4, y = 10. how do you find y when x = 8?

Answer 1

`color(red)(y=5` when `color(blue)(x=8)`

Explanation:

If `y` varies inversely as twice `x`, then
`color(white)("XXX")color(blue)y=color(magenta)c/(2color(green)x)color(white)("xxx")`for some constant `color(magenta)c`

We are told that `color(green)x=color(green)4`, `color(blue)y=color(blue)(10)` is a solution to this relation.
so
`color(white)("XXX")color(blue)10=color(magenta)c/(2 * color(green)4)`

`color(white)("XXX")rarr color(magenta)c=80`

Therefore the relation is
`color(white)("XXX")color(blue)y=color(magenta)(80)/(2color(green)x)`

When `color(green)x=color(green)8`, we have
`color(white)("XXX")color(blue)y=color(magenta)(80)/(2 * color(green)8) = 5`