SOLUTION: Diaphanous was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century C.E. When he died, someone described his life in this puzzle. H

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Question 630693: Diaphanous was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century C.E. When he died, someone described his life in this puzzle. He was a boy for 1/6 of his life. After 1/12 more, he acquired a beard. After another 1/7, he married. In the fifth year after his marriage, his son was born. The son lived half as many years as his father. Diaphanous died 4 years after his son. How old was Diaphanous when he died?
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Diaphanous was a famous Greek mathematician who lived and worked in Alexandria, Egypt, probably in the third century C.E. When he died, someone described his life in this puzzle. He was a boy for 1/6 of his life. After 1/12 more, he acquired a beard. After another 1/7, he married. In the fifth year after his marriage, his son was born. The son lived half as many years as his father. Diaphanous died 4 years after his son. How old was Diaphanous when he died?

Let Diaphanous’ age when he died be D
He was a boy for 1%2F6 of D, or D%2F6
Since after 1%2F12 more years, or D%2F12, he acquired a beard, then he acquired a beard at age: D%2F6+%2B+D%2F12, or %282D+%2B+D%29%2F12, or 3D%2F12, or D%2F4
Since after 1%2F7 more years, or D%2F7, he got married, then he got married at age: D%2F4+%2B+D%2F7, or %287D+%2B+4D%29%2F28, or 11D%2F28
Since his son was born 5 years after he got married, then his son was born when he was: 11D%2F28+%2B+5
Since son lived for ½D, or D%2F2, then Diaphanous was 11D%2F28+%2B+5+%2B+D%2F2 when his son died
Since he died 4 years after his son’s death, he died at age 11D%2F28+%2B+5+%2B+D%2F2+%2B+4, or 11D%2F28+%2B+D%2F2+%2B+9. The age that he died is also D
Therefore, 11D%2F28+%2B+D%2F2+%2B+9+=+D
11D + 14D + 252 = 28D ------ Multilpying by LCD, 28
11D + 14D – 28D = - 252
- 3D = - 252
D, or age that Diaphanous died at was: %28-+252%29%2F-+3, or highlight_green%2884%29

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Check
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Lived for 84 years
Boy for 1%2F6 of 84, or 14 years
After 1%2F12 of 84, or 7 years, he acquired a beard. Acquired beard @ age 21 (14 + 7)
After 1%2F7 of 84, or 12 years, he got married. Got married @ age 33 (21 + 12)
After 5 years of marriage, his son was born. Son was born @ age 38 (33 + 5)
Son lived for ½ of 84, or for 42 years. Age at son’s death = 80 (38 + 42)
He died 4 years after son’s death. Died at age 84 (80 + 4)

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