Question 139565
Let x = the number of sons. x - 1 would be the number of brothers each son has so each son would then have x-1 sons of his own, making for a total of x(x-1) grandsons. 

So adding the number of sons (x) to the total number of grandsons x(x-1) you get the expression {{{x + x(x-1)}}}, or {{{x + x^2 - x}}} or simply x^2.

You know x^2 lies somewhere between 50 and 80 so the equation becomes

{{{50 < x^2 < 80}}}. The only perfect square that falls between 50 and 80 is 64 which is 8^2. Therefor, x = 8, which is the number of sons.

We showed above that the number of grandsons is x(x-1) or 8(8-1) or 8*7 which is 56 grandsons. So the grandfather has 8 + 56 = 63 total sons and grandsons, which is also his age.