Solution for #18

Alternate Solution #1

Let x be the age of the man at the time of his death. His age consists of the number of years he spent as a child plus the number of years he spent as a teenager plus the number of years between his coming of age and his marriage plus five plus his son's age (half his own) plus four. In mathematical terms, this is:

                      x = x/6 + x/12 + x/7 + 5 + x/2 + 4
                      x = 14x/84 + 7x/84 + 12x/84 + 42x/84 + 9
                      x = 75x/84 + 9
        84x/84 - 75x/84 = 9
                  9x/84 = 9
                   x/84 = 1
                      x = 84 

So the man lived to be 84 years old.

Alternate Solution #2

The man lived 1/12 of his life as a teenager. There are seven teen years. 7 × 12 = 84.