Pedro's barn and how to find constant

Question

"In Pedro's barn, the number of mice is inversely proportional to the number of cats. When he owned 5 cats, there were 48 mice in the barn. He increased the number of cats to 8. Based on the increased number of cats, how many mice are in the barn? Assuming that the relationship between the number of nice and the number of cats does not change, write an equation that Pedro could to to determine the number of mice (m), for any number if cats (c)."

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I know what inversely proportional means. I know that in this case, as the number of cats increases, the number of mice decreases. I also know that the equation would be: m=k/c, k=constant. I need to know how to find the constant, and the steps leading up to it. Thanks.

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Edit: I figured it out, thanks for your help anyway.

Answer 1

We have that $$5=\frac k{48} \implies k= 240$$ and $$m=\frac{240}c$$ with $c=8$. The result is then $m=30$.

Answer 2

You find the constant by substituting the known values into the equation $m=\dfrac{k}{c}$:

$$48=\dfrac{k}{5}\implies k=240.$$