Diophantus' Riddle
Here lies Diophantus, the wonder behold......
Through art algebraic,the stone tells how old;
God gave him his boyhood 1/6 of his life,
1/12 more as youth while whiskers grew rife;
And the 1/7 ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage.
After attaining half of his father's age,
Chill fate took him.
Grieved and full of tears,
He passed on after four years.
Find Diophantus' age at death. (Source from textbook)
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1 solution
Stated in prose, the poem says that Diophantus's youth lasts 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, Diophantus married. Five years later, he had a son. The son lived exactly half as long as his father, and Diophantus died just four years after his son's death. All of this totals the years Diophantus lived.
Let D be the number of years Diophantus lived, and let S be the number of years his son lived. Then the above word problem gives the two equations
D = (1/6+1/(12)+1/7)D+5+S+4 (1)
S = 1/2D. (2)
Solving this simultaneously gives S=42 as the age of the son and D=84 as the age of Diophantus.