Question 1180969: when Mrs jones was older than 50 but younger than 80, she 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 both my sons and grandsons."
Answer by ikleyn(52803)   (Show Source):
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when Mrs jones was older than 50 but younger than 80, she 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 both my sons and grandsons."
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Let n be the number of her sons.
Each of the sons has (n-1) brothers.
So, to answer the problem's question, we should solve this inequality
50 < n*(n-1) + n < 80
or, equivalently,
50 < n^2 < 80,
which gives a unique solution n = 8.
So, her age is n*(n-1) + n = n^2 = 8^2 = 64. ANSWER
Solved, answered, carefully explained and completed.
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