+87 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 are2r+1 mice, and when there are 6r-27 mice, there arer-5 cats. Find K.
Please help fast. Thank you! :)
3 r - 19 = k/(2 r + 1) ............(1)
6 r - 27 = k/(r - 5) ...............(2)
r =7 and k =30
Some people seem to have some difficulty in understanding how r=7 and k=30 were obtained above!!!.
Solve for k in equation (1) above and you should get this:
k = 6 r^2 - 35 r - 19
Solve for k in equation (2) above and you should get this:
k = 6 r^2 - 57 r + 135
Equate the above 2 equations and solve for r:
6 r^2 - 57 r + 135 = 6 r^2 - 35 r - 19, solve for r
-57r +35r =-19 - 135
-22r = - 154
r = 7 sub this into one of the equations above and you should get:
k = 30
+87 I check the work by just plugging it into the equation, but the work helps alot. Thank you for all the help! 
