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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 $6r-24$ mice, there are $r-3$ cats. Find $k$.

 Jan 24, 2021
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3 r - 19 = k/(2 r + 1) ............(1)

6 r - 24 = k/(r - 3) ...............(2)

 

r =9 and k = 152

 Jan 24, 2021

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