document.write( "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.\" \n" ); document.write( "

Algebra.Com's Answer #810801 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "when Mrs jones was older than 50 but younger than 80, she told a friend,
\n" ); document.write( "\"each of my sons has as many sons as brothers, and the number of my years
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document.write( "Let n be the number of her sons.\r\n" );
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document.write( "Each of the sons has (n-1) brothers.\r\n" );
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document.write( "So, to answer the problem's question, we should solve this inequality\r\n" );
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document.write( "    50 < n*(n-1) + n < 80\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "    50 < n^2 < 80,\r\n" );
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document.write( "which gives a unique solution  n = 8.\r\n" );
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document.write( "So, her age is  n*(n-1) + n = n^2 = 8^2 = 64.    ANSWER\r\n" );
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