SOLUTION: Here you see the tomb of Diophantis 1/6 of his life god granted him youth. After 1/12 more his cheeks were bearded. After an additional 1/7 he kindled the light of marriage. In t

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Question 83824: Here you see the tomb of Diophantis 1/6 of his life god granted him youth. After 1/12 more his cheeks were bearded. After an additional 1/7 he kindled the light of marriage. In the 5th year of marriage he fathered a son. Alas, the sons life span was only 1/2 that of his fathers, who grieved during the remaining 4 years of his life. By the device of Alegbra, tell the extent of both Diaphantis and his sons life.
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Here you see the tomb of Diophantis 1/6 of his life god granted him youth. After 1/12 more his cheeks were bearded. After an additional 1/7 he kindled the light of marriage. In the 5th year of marriage he fathered a son. Alas, the sons life span was only 1/2 that of his fathers, who grieved during the remaining 4 years of his life. By the device of Alegbra, tell the extent of both Diaphantis and his sons life.

Let L = Diophantis' life span (age at death).

...1/6 of his life god granted him youth...

1%2F6L = his youth years

...After 1/12 more his cheeks were bearded...

So his cheeks bearded at age 1%2F6L + 1%2F12L

...After an additional 1/7 he kindled the light of marriage...

So he married at age 1%2F6L + 1%2F12L + 1%2F7L

...In the 5th year of marriage he fathered a son...

So he fathered a son at age 1%2F6L + 1%2F12L + 1%2F7L + 5

...Alas, the son's life span was only 1/2 that of his fathers...

So when his son died his (Diophantis') age was 1%2F6L + 1%2F12L + 1%2F7L + 5 + 1%2F2L

...who grieved during the remaining 4 years of his life...

So Diophantis died at age: 1%2F6L + 1%2F12L + 1%2F7L + 5 + 1%2F2L + 4

And that must equal to his total lifespan L:

1%2F6L + 1%2F12L + 1%2F7L + 5 + 1%2F2L + 4 = L

Multiply by the LCD of 84

841%2F6L + 841%2F12L + 841%2F7L + 84·5 + 841%2F2L + 84·4 = 84L

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

75L + 756 = 84L

75L - 84L = -756

       -9L = -756

         L = 84.

So Diophantis lived to be 84.

...1/6 of his life god granted him youth...

1%2F6L = = 14 his youth years

...After 1/12 more his cheeks were bearded...

So his cheeks bearded at age 1%2F6L + 1%2F12L = 21

...After an additional 1/7 he kindled the light of marriage...

So he married at age 1%2F6L + 1%2F12L + 1%2F7L = 33

...In the 5th year of marriage he fathered a son...

So he fathered a son at age 1%2F6L + 1%2F12L + 1%2F7L + 5
= 38
...Alas, the son's life span was only 1/2 that of his fathers...

So when his son died his (Diophantis') age was 1%2F6L + 1%2F12L + 1%2F7L + 5 + 1%2F2L = 80

Which means his son only lived to be 42.

Then Diophantis died 4 years later at age 84.

Edwin