At the AoPS office, mice vary inversely with cats, that is, {mice}={k}/{cats}, for some value of $k$. When there are $3r-19$ cats, there are $2r+1$ mice, and when there are $6r-27$ mice, there are $r-5$ cats. find k
2r+1 = k /(3r-19)............(1)
6r - 27 = k /(r - 5)...........(2), solve for k, r
k =6 r^2 - 35 r - 19 - from (1) above
k =6 r^2 - 57 r + 135 - from (2) above
6 r^2 - 35 r - 19 =6 r^2 - 57 r + 135
6 r^2 - 35 r - 19 - 6 r^2 + 57 r - 135 =0
22r - 154 =0
22r = 154
r = 7
k = 30
2r+1 = k /(3r-19)............(1)
6r - 27 = k /(r - 5)...........(2), solve for k, r
k =6 r^2 - 35 r - 19 - from (1) above
k =6 r^2 - 57 r + 135 - from (2) above
6 r^2 - 35 r - 19 =6 r^2 - 57 r + 135
6 r^2 - 35 r - 19 - 6 r^2 + 57 r - 135 =0
22r - 154 =0
22r = 154
r = 7
k = 30
