Question 1171186
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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.<br>
First look at the statement "In five years, the product of her age and son’s age two years ago will be 35."<br>
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.<br>
The statement should read "The product of her age 5 years from now and her son's age two years ago is 35."<br>
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.<br>
But that answer is incompatible with the other given information, because the other information is given incorrectly.<br>
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.<br>
"ten times AS OLD AS x" means 10 times x, or 10x.<br>
"ten times OLDER THAN x" means x, plus 10 more times x, which is x+10x = 11x.<br>
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.<br>
So the bottom line on this problem is that there is no solution the problem as given.<br>