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\n" ); document.write( "The statement of the problem is awkward and open to different interpretations; and the problem only has a solution if an invalid interpretation is used.
\n" ); document.write( "First look at the statement \"In five years, the product of her age and son’s age two years ago will be 35.\"
\n" ); document.write( "The two ages in that statement are undoubtedly the mother's age 5 years from now and the son's age 2 years ago. But, because of the awkward phrasing, it could also be interpreted as the mother's age 5 years from now and the son's age 2 years BEFORE THAT, which would be 3 years from now.
\n" ); document.write( "The statement should read \"The product of her age 5 years from now and her son's age two years ago is 35.\"
\n" ); document.write( "Given that interpretation, the only sensible answer is that the mother's age 5 years from now will be 35 and her son's age 2 years ago was 1; that makes her age now 30 and her son's age now 3.
\n" ); document.write( "But that answer is incompatible with the other given information, because the other information is given incorrectly.
\n" ); document.write( "Unfortunately, in everyday usage, \"ten times as old as\" and \"ten times older than\" are used to mean the same thing; but they do not.
\n" ); document.write( "\"ten times AS OLD AS x\" means 10 times x, or 10x.
\n" ); document.write( "\"ten times OLDER THAN x\" means x, plus 10 more times x, which is x+10x = 11x.
\n" ); document.write( "In the given problem, the answer that the mother is 30 and the son is 3 means that the mother is 10 times AS OLD AS her son. But the problem says she is 10 times OLDER THAN her son; and that is not true.
\n" ); document.write( "So the bottom line on this problem is that there is no solution the problem as given.
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