At the AoPS office, mice vary inversely with cats, that is, $\text{mice}=\frac{k}{\text{cats}}$, for some value of $k$. When there are $3r-19$ cats, there are $2r+1$ mice, and when there are $6r-24$ mice, there are $r-3$ cats. Find $k$.
3 r - 19 = k/(2 r + 1) ............(1)
6 r - 24 = k/(r - 3) ...............(2)
r =9 and k = 152
