Question

How do you write the equation if P varies inversely as Q and Q = 2/3 when P = 1/2?

Answer 1

If P varies inversely as Q then
`color(white)("XXXXX")` `P*Q = c`
`color(white)("XXXXX")` `color(white)("XXXXX")` for some constant `c`

Given that `(P,Q)=(1/2,2/3)` is a solution to this equation we have

`color(white)("XXXXX")` `(1/2)*(2/3) = c`
`color(white)("XXXXX")` `rarr c = 3`

So the required equation is
`color(white)("XXXXX")` `P*Q = 3`