# Pedro's barn and how to find constant

"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)."

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.

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

• Find the constant, $k$, using the values for $m,c$ given in the initial situation. $48$ and $5$. – turkeyhundt Feb 12 '15 at 1:27
• Wellm you know one pair of values, $m,c$... – Thomas Andrews Feb 12 '15 at 1:27
• @Dana Maybe you could write down an answer? So the question doesn't remain answered. – Tejas Feb 12 '15 at 2:19

## 2 Answers

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

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

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