please help me

Question

Diophantus spent 1/6 of his life in childhood, 1/12 as a youth, and 1/7 more as a bachelor. Five years after his marriage was born a son who died four years before his father at half the age at which his father died. How old was Diophantus when he died?

Answer 1

Let D= the number of years Diophantus lived. Let S= the number of years his son lived. 

 

Diophantus lived 1/6 of his years in childhood, 1/12 of his years in youth, and 1/7 of his years as a batchelor. He lived five more years before his son was born. He lived the same number of years that his child did and then lived four more years after his son died.

 

D= (1/6)D + (1/12)D + (1/7)D + 5 + S + 4

 

His son lived half the number of years as his father.

 

S=(1/2)D

 

Substitute this into the first equation so that there is only one variable.

 

D = (1/6)D + (1/12)D + (1/7)D + 5 + (1/2)D + 4

 

Multiply each term by the Least Common Denominator (the smallest number that all of the denominators go into evenly), which is 84.

 

84D = 84(1/6)D + 84(1/12)D + 84(1/7)D + (84)(5) + 84(1/2)D + 84(4)

 

84D = 14D + 7D + 12D + 420 + 42D + 336

 

Subtract 14D, 7D, 12D and 42D from both sides of the equation.

 

9D = 420 + 336

 

9D = 756

 

Divide both sides of the equation by 9.

 

D= 84

 

Therefore, Diophantus was 84 years old when he died. Since the question does not clarify about whom the pronoun "he" refers, it is possible that the question is asking, "How old was Diophantus when his son died?" In this case, Diophantus was 80 when his son died.