For first sixth of his life, Diophantus was boy. After twelfth of his life, Diophantus grew beard. One-seventh of his life after this, Diophantus married. Five years after his marriage, Diophantus's son was born. Diophantus's son died at the relatively young age. Four years after his so died, Diophantus himself died. The total number of years the son lived is one-half the total number of years Diophantus lived.
a) Write one or more equations that express the information in the riddle algebraically.
b) Sove your equation(s) from part a to determine the following:
- The total number of years Diophantus lived
- The number of years Diophantus spent as a boy
- The age at which Diophantus grew a beard
- The are at which Diophantus got married
- Diophantus's age when his son was born
- Diophantus's age when his son died