P = N 19 - C The given equation relates the positive numbers P , N

Choice D is correct. It's given that the values of $P$, $N$, and $C$ are positive. Therefore, dividing each side of the given equation by $N$ yields $\frac{P}{N}=19-C$. Subtracting $19$ from each side of this equation yields $\frac{P}{N}-19=-C$. Dividing each side of this equation by $-1$ yields $19-\frac{P}{N}=C$, or $C=19-\frac{P}{N}$.

Choice A is incorrect. This equation is equivalent to $P=NC-19$, not $P=N\left(19-C\right)$.

Choice B is incorrect. This equation is equivalent to $P=19-NC$, not $P=N\left(19-C\right)$.

Choice C is incorrect. This equation is equivalent to $P=N\left(C-19\right)$, not $P=N\left(19-C\right)$.