Math problem puzzle

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 ?

It's really simple : The above system of 3 equations in 3 unknowns can be solved as follows.

I know the solution should i write it ?

Answer 1

Assuming $x, y,\text{ and } z$ are the ages of your grandson, your son, and you respectively, expressed in years, then your system is:

$$365x = 52y$$ $$12x=z$$ $$x+y+z=120$$

Therefore $x=6$, $y=42$ and $z=72$

Answer 2

Your son is $7$ times as old as your grandson. You are $12$ times as old as your grandson. Therefore if you let $x$ denote the age of your grandson, you have $$x + 7x + 12x =20x = 120$$ It follows that your grandson is $6$ years old, your son is $42$ years old and you are $72$ years old.