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My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

Verified Answer :

ValyRemus

Let m be my age in years.
If s is my son's age in years, then my son is 52s weeks old. If g is my
grandson's age in years, then my grandson is 365g days old. Thus,

365g = 52s.

Since my grandson
is 12g months old,

12g = m.

Since my grandson,
my son and I together are 120 years,

g + s + m = 120.

The above system of
3 equations in 3 unknowns (g, s and m) can be solved as follows.

m / 12 + 365 m /
(52 x 12) + m = 120 or

52 m + 365 m + 624
m = 624 x 120 or

m = 624 x 120 /
1041 = 72.
So, I am 72 years
old. 

The problem is hard...i don't know if you understood this..Hope i helped!

naǫ

x - your son's age in years
y - your age in years

There are 52 weeks in a year and 365 days in a year, so the age of your grandson in years is (52x)/365
There are 12 months in a year, so the age of your grandson in years is y/12.

Set both expressions equal to each other:
\(\frac{52x}{365}=\frac{y}{12} \\ 52x \times 12=365y \\ 624x=365y \\ x=\frac{365}{624}y\)
Your son's age is equal to 365/624 of your age.

Your grandson, your son and you together are 120 years.
\(\frac{1}{12}y+\frac{365}{624}y+y=120 \\ \frac{52}{624}y+\frac{365}{624}y+\frac{624}{624}y=120 \\ \frac{1041}{624}y=120 \\ y=120 \times \frac{624}{1041} \\ y \approx 72\)

You are 72 years old.

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