SOLUTION: when grandpa was over fifty but less than eighty, he told a friend, "each of my sons has as many sons as brothers, and the number of my years is exactly that of the number of all m

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Question 139565: when grandpa was over fifty but less than eighty, he told a friend, "each of my sons has as many sons as brothers, and the number of my years is exactly that of the number of all my sons and grandsons." how many sons and grandsons does grandpa have?
Answer by frostusna(7) About Me  (Show Source):
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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+%2B+x%28x-1%29, or x+%2B+x%5E2+-+x or simply x^2.
You know x^2 lies somewhere between 50 and 80 so the equation becomes
50+%3C+x%5E2+%3C+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.