# There are 172 South American animals in a zoo. That number is more than 1/2 the number of African animals. If n is the number of African animals, what does n equal?

$S A > \frac{1}{2} n$

#### Explanation:

We can't find the number exactly, but we can find a range of possible answers.

We know that the number of South American animals in the zoo is 172 and that number is more than $\frac{1}{2}$ of the number of African animals. I'll use SA as South American animals and A as African animals (I'll call it $n$ at the end to match up with the question's request). We can say:

$S A > \frac{1}{2} A$

and so therefore:

$A < 2 S A$

We can drop in the number for SA:

$A < 2 \left(172\right) = 344$

Now - we now the maximum number of African animals is less than 344. We can also presume that the minimum number of African animals is bigger than 172 (otherwise the question would have been phrased differently). So the overall answer is:

$172 < A < 344$ and to meet the requirement of the question, I'll put it in terms of $n$:

$172 < n < 344$