### Brain Teasers

# How Old, Again?

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?

### Hint

Round is allowed on final answer### Answer

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.a+b+c=140

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

12c=a

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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