Facing Some Challenges of Age

The Problem Mike and Ike are good friends and like to challenge new acquaintances with the following riddle, saying that they ll pick up the tab at the restaurant if the riddle can be solved. Here s what they pose to the unsuspecting Mike is twice as old as Ike was when Mike was as old as Ike is now. Right now, Mike is 36 years old. How old is Ike right now  

The most common plan of action is to let Ike s age be represented with x and then write some expressions and equations involving that variable. In this case, because you know Mike s age already, it makes more sense to figure out how many years ago the riddle is referring to — solve for x. Here s what you know  

Does that look like sleight-of-hand Look at Table 15-1, showing possible ages of Mike and Ike if x is the number of years since Ike was 18. 

Nine years ago, Mike was 27, which is the same age that Ike is now. When Mike was 27, Ike was 18 (or half Mike s age now). If I had just written the equation 36 - x = 18 + x and solved it to get 18 = 2x or x = 9, you might not have believed me. For the naturally skeptical, Table 15-1 helps. 

The next problem uses more number theory than algebra. Haul out your prime factorizations to do this problem. 

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