## Monday, September 18, 2006

### How old?

The grandson is about as many days old as the son is in weeks. The grandson is approximately as many months old as the father is in years. The ages of the grandson, the son, and the father add up to 120 years. What are their ages?

1. There are some fractional years that (as in normal conversation) I will truncate.

Father - 72
Son - 42
Grandson - 6

Using the following equations:

Y(F) + Y(S) + Y(G) = 120
Y(S) = 365/52 Y(G) (frational results)
Y(F)= 12Y(G)

Substitution yields the Grandson is just over 6 years old.

2. Or you could set up the ratio:

1:7:12

(weeks = days means the ratio of their ages is 7:1, months = days, 12:1)

so x + 7x + 12x = 120

3. Both answers make sense to me.

The father is 72, the son is 42, and the grandson is 6 years old.

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