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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 $6r-27$ mice, there are $r-5$ cats. Find $k$.

 Jan 8, 2021
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https://web2.0calc.com/questions/confusing-algebra: Link To Actuall Response

 

 

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

 Jan 8, 2021

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