Question

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 ?

Answer 1

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!

Answer 2

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:

`(52x)/(365)=(y)/(12) \\ 52x * 12=365y \\ 624x=365y \\ x=(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.

`(1)/(12)y+(365)/(624)y+y=120 \\ (52)/(624)y+(365)/(624)y+(624)/(624)y=120 \\ (1041)/(624)y=120 \\ y=120 * (624)/(1041) \\ y \approx 72`

You are 72 years old.