Question

P varies directly with Q and inversely with R. P=9, when Q=3 and R=4. How do you find Q when P=1 and R=1/2?

Answer 1

`Q=1/24`

Explanation:

If `P` varies directly with `Q` and inversely with `R` then
`color(white)("XXX")(P * R)/Q=k` for some constant `k`

If `P=9, Q=3, and R=4` then
`color(white)("XXX")(9 * 4)/3=kcolor(white)("xx")rarrcolor(white)("xx")k=12`

So when `P=1` and `R=1/2`
`color(white)("XXX")(1 * 1/2)/Q=12`

`color(white)("XXX")1/2=12Q`

`color(white)("XXX")Q=1/24`