9514 1404 393
Answer:
72
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
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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.
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Additional comment
We've already seen my son is 6. My daughter is 42.