SOLUTION: I need a little help with this word problem. I have tried to fiugre out how to write it out into algebraic form...but have been unsuccessful. Any help would be appreciated. The

Question 27432: I need a little help with this word problem. I have tried to fiugre out how to write it out into algebraic form...but have been unsuccessful. Any help would be appreciated.
The inscription on Greek Diophantus' tomb:
One-sixth of his life God granted him youth. After a twelfth more, he grew a beard. After an additional seventh, he married, and 5 years later, he had a son. Alas, the unfortunate son's life span was only one-half that of his father, who consoled his grief in the remaining 4 years of his lfe.
Use your knowledge to find how many years Diophantus lived. (HINT: let x be the number of years Diophantus lived.)
Again thanks for the help.
Found 2 solutions by wuwei96815, Paul:
Answer by wuwei96815(245) (Show Source):
You can put this solution on YOUR website!
The wording of the problem is not totally clear. For instance, "After a twelfth more, ...." Does that refer to 1/12 of his total life or some other number? Anyway, I will give it a try.

1/6x + 1/12x + 1/7x + 5 + 4 = 1/2x
Multiply each term by a common denominator, in this case 84.
14x + 7x + 12x + 420 + 336 = 42x
Combine like terms.
420 + 336 = -14x - 7x -12x + 42x
756 = 42x
18 = x

Did I do something wrong? The answer doesn't seem logical.

Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!
Let x be his age:
After = + and 5 years after means that add 5 to current status:
1x/6+1x/12+1x/7+5+4=1x/2
Common denominator = 84
14x+7x+12x+420+336=42x
Simplfy
33x+756=42x
9x=756
x=84

Hence, he lived for 84 years.
Paul.