SOLUTION: On his last birthday, Grandfather claimed that he had lived 1/7 of his life as a boy, 1/12 as a teenager, 2/3 as a man and spent 9 years in old age. How old was Grandfather on his

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Question 1093381: On his last birthday, Grandfather claimed that he had lived 1/7 of his life as a boy, 1/12 as a teenager, 2/3 as a man and spent 9 years in old age. How old was Grandfather on his last birthday?
Found 3 solutions by josmiceli, ikleyn, richwmiller:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = his age on last birthday

Miultiply both sides by




----------------
He was 84 on last birthday
----------------------------
check:




OK
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let x be the Grandfather age.


Then you have this equation from the condition

 = x.


Multiply both sides by 7*12 = 84 to rid of denominators

12x + 7x + 56x + 9*84 = 84x,

75x + 9*84 = 84x,

9*84 = 84x - 75x  ====>  9*84 = 9x  ====>  x = 84.

Answer. Grandfather was 84 years old. 


          Notice that 7*12 = 84, therefore, one could suggest/guess the answer without calculations.


To wider your horizon, there is very similar poetical mathematical legend from ancient times for the same theme and melody.

http://mathworld.wolfram.com/DiophantussRiddle.html



Also see these links in this forum

https://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.244899.html

https://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.427066.html



Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!

The answer 84 can be obtained from two of the clues.
1/7 of his life as a boy
1/7 x=12
x=84
Teenagers are from 13 to 19 for a total of 7 years
x/12=7 again 84
The last two clues are misleading.
2/3x as a man 2/3(84)=56
84-56=28 since when does manhood begin at 28?
Since when is age 75 the beginning of old age?
AARP accepts members at age 50.
Retirement with Social Security begins at 67.
A cute puzzle but misleading.




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