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How Old, Again?

Math brain teasers require computations to solve.


Puzzle ID:#49426
Fun:*** (2.69)
Difficulty:*** (2.22)
Submitted By:fishmedAus******mod




Suppose I am a grandfather. My grandson is about as old in days as my son is in weeks. He is also as many months old as I am in years. Together, the three of us are 140 years old. How old am I?

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As noted, all three are 140 years old. Thus, a+b+c=140, where a is grandfather, b is son, and c is grandson. Additionally, grandson being about as many days old as son is in weeks gives 365c=52b. Finally, the grandson being as many months as I am in years gives 12c=a. Thus, the following are known.

365c=52b or b=365c/52

By calculation and substitution we have as follows.

12c + 365c/52 +c = 140
624c + 365c + 52c = 7280
1041c = 7280
c = 6.99, or 7 (teaser said 'about')
so, as 12c = a, then a = 84.

I am 84 years old.
As an aside, my son is 49.


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Oct 07, 2012

Very cleverly worded. A good one. Took a few minutes to solve.
Aug 01, 2013

Well done and tricky
Dec 02, 2013

I took "My grandson is about as old in days as my son is in weeks. He is also as many months old as I am in years."
to mean

MY SON is as many months old as I am in years...but when that gave my age as being over 140 years old, I reread the question and got the correct anwer
Jan 06, 2014

perfect :-P
Feb 23, 2014

My way to solve: Say grandson is 1. Son would be 7 and grandfather 12. Adds up to 20. So multiply everything by 7 to make the sum 140: 7, 49, 84.
Sep 26, 2015

Since the son is as many weeks old as the grandson is days old, then S = 7Gs. Likewise, the grandfather is as many years old as the grandson is months old, so G = 12 Gs. So 12Gs + 7Gs + Gs = 140, 20Gs = 140, Gs = 7. 7Gs = 49, and 12Gs = 84.

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