How To solve This Perfect Square Word Problem Here's a problem about perfect squares and it's very hard for me. I tried to solve but I got stuck.
Last year, the town of Whipple had a population that was a perfect square. Last month, 100 enlightened people moved to Whipple, making the population one more than a perfect square. Next month, 100 more people will move to Whipple, making the population a perfect square again. What was the original population of Whipple?
Here's what I did:
Let the population last year be n, so n = x^2 and x = √n
Last month: n + 100 = x^2 + 1
Next Month: n + 200 = x^2 ...
and i Got stuck there. I don't know where I am going ... Your help is appreciated

I like where Will Jagy starts.
$$x^2+99 = y^2\\
x^2 + 200 = z^2$$
to continue I would subtract one from the other
$$z^2 - y^2 = 101\\(z+y)(z-y) = 101$$
$101$ is prime
$$z+y = 101\\z-y = 1\\z = 51\\y = 50\\x = \sqrt{51^2 - 200} = 49$$
