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! :)

thunderkirby
Aug 10, 2018

#1**+1 **

3 r - 19 = k/(2 r + 1) ............(1)

6 r - 27 = k/(r - 5) ...............(2)

r =7 and k =30

Guest Aug 10, 2018

#4**+1 **

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

Guest Aug 11, 2018

#6**+1 **

I check the work by just plugging it into the equation, but the work helps alot. Thank you for all the help!

thunderkirby
Aug 11, 2018