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

9514 1404 393

  72

Step-by-step explanation:

Let x, y, z represent my age, my daughter's age, and my grandson's age in years. We assume for this problem 365 days in a year, so 52 1/7 weeks in a year.

  x + y + z = 120 . . . . the total of our ages in years

  12z = x . . . . . . . . . . . my grandson's months are the same as my years

  365z = (52 1/7)y . . . grandson's days = daughter's weeks

__

Writing these equations in standard form, we have ...

  x + y + z = 120

  x + 0y -12z = 0

  0x +y -7z = 0

These can be solved by a variety of methods. A "by-hand" solution follows.

Subtracting the last two equations from the first, we get

  (x +y +z) -(x -12z) -(y -7z) = (120) -(0) -(0)

  20z = 120

  z = 6

Then x can be found from the second equation:

  x = 12z = 12(6) = 72

My age is 72 years.

Additional comment

We've already seen my son is 6. My daughter is 42.

fdvs

step-by-step explanation: vsfdvsfvd