I came across this puzzle in a bunch of old forwarded e-mails and just had to solve it:
Diophantus passed 1/6th of his life in childhood, 1/12th in youth and 1/7th as a bachelor. 5 years after his marriage, there was born a son who died 4 years before his father, at half his father's final age.
How old was Diophantus when he died?
Ok, so this is one of those word problem things. I worked it out by drawing timelines of the father and son and labelling each section with values provided in the problem - either in years, or as fractions of f (the father's age of death) or s (the son's age at death).
This gave me an equation with f on one side (which I wanted to solve for) but a sum of fractions with f in the numerator and uncommon denominators on the right side.
That's pretty much where I got stuck. I couldn't remember what sort of tools I could use to simplify the equations... I tried dividing both sides by f, but I'm not sure if I did it right. Then I tried subtracting a fraction from both sides but again I'm not sure I did it right. I ended up with something that looked like it was going to come out with a negative value so I knew I messed up somewhere.
So I went online looking for an equation solver. Boy oh boy, look what I found!
DiscoverySchool.com's Linear Equation Solver not only solved the equation - it showed me HOW to solve it!
Here is the solution.
That's so cool. :)