1331.12 – Louie's Age

Louie won't tell you his age. But, if you happen to square his age this year, and square his age next year, the difference between these two perfect squares is 75. So how old is Louie?

Solution

This can be done by guessing. It can also be done with a spreadsheet. And then there is algebra:

(x+1)2−x2=75,x2+2x+1−x2=75,2x+1=75⇝x=37. \begin{aligned} (x+1)^2 - x^2 &=& 75, \\ x^2 + 2x + 1 -x^2 &=& 75, \\ 2x + 1 &=& 75 \leadsto x = 37. \end{aligned}