Question

If y varies inversely as x, how do you find x when y = 3 if y = 15 when x = 2?

Answer 1

`x=10`

Explanation:

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

We are told when `color(red)(x=2)` then `color(blue)(y=15)`
So
`color(white)("XXX")color(red)(2)*color(blue)(15)=color(green)(c)`

`color(white)("XXX")rArr color(green)(c=30)`
and
`color(white)("XXX")color(red)color(red)(x)*color(blue)(y)=color(green)(30)`

Therefore when `color(blue)(y=3)`
`color(white)("XXX")color(red)(x)*color(blue)(3)=color(green)(30)`
`color(white)("XXX")rarr color(red)(x) = 10`