smc

Let $x$ be the population in $1996$, and let $k$ be the constant of proportionality. If $n=1994$, then the difference in population between $1996$ and $1994$ is directly proportional to the population in $1995$. Translating this sentence, $(x-39)=k(60)$ Similarly, letting $n=1995$ gives the sentence $(123-60)=kx$ Since $kx=63$, we have $k=\frac{63}{x}$ Plugging this into the first equation, we have: $(x-39)=\frac{60\cdot 63}{x}$ $x-39=\frac{3780}{x}$ $x^2-39x-3780=0$ $(x-84)(x+45)=0$ Since $x>0$, we must have $x=84$, and the answer is $\boxed{84}$.