How Long Did Diophantus Live?

[nycmath]

"Here lies Diophantus," the wonder behold... Through art algebraic, the stone tells how old:"God gave him his boyhood one-sixth of his life, One-twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, this dear child of master and sage, Attained only half of his father’s full age. When chill fate took him — an event full of tears —Heartbroken, his father lived just four more years." How long did Diophantus live?

[Eigenvalue]

Let x be Diophantus' age and y be the son's age
[tex]\frac{1}{6}[/tex]x+[tex]\frac{1}{12}[/tex]x+[tex]\frac{1}{7}[/tex]x+5+y+4=x
x=2y

[tex]\frac{14+7+12}{81}[/tex]x+9+y=x
[tex]\frac{33}{84}[/tex]x+9=x
y+9=[tex]\frac{51}{84}[/tex]x
y+9=[tex]\frac{102}{84}[/tex]y
9=[tex]\frac{18}{84}[/tex]y
y=42
x=84