<PRE><B>Question 1139570</B>
&lt;br&gt;
This is a good example of a problem that is solved far more easily by logical reasoning than by formal mathematics.&lt;br&gt;
The problem says that the man is 7 years older than his wife; and it asks when the product of their ages &lt;u&gt;WILL BE&lt;/u&gt; 2150.&lt;br&gt;
2150 = 50*43; so the time when their ages are 50 and 43 is some time in the future.&lt;br&gt;
That, along with the information that the sum of the digits of the man&#39;s age is 10, means the man currently can be only 19, 28, 37, or 46.  So try those possible ages for the man and see which one fits the conditions of the problem.&lt;br&gt;&lt;pre&gt;
                        man&#39;s current age:  19  28  37  46
                       wife&#39;s current age:  12  21  30  39
                    man&#39;s age 5 years ago:  14  23  32  41
                   wife&#39;s age 5 years ago:   7  16  25  34
  wife&#39;s age 5 years ago, digits reversed:  --  61  52  43&lt;br&gt;&lt;/pre&gt;
The table shows that if the man is now 46, his age 5 years ago was 2 less than the age of his wife then with the digits reversed.&lt;br&gt;
So the man is currently 46; he will be 50 in 4 years.&lt;br&gt;
ANSWER: The product of their ages will be 2150 4 years from now.</PRE>