1) Three generations
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 in years.
let the age of the grandson be x days
so the age of the son is x weeks
and the age of the father is x/30 years
so,...
Grandson = x days = x/30 months = x/365 years
Son = x weeks = x/5s years
father = x/30 years
then x/30 + x/52 + x/365 = 120
x(1/30 + 1/52 + 1/365) = 120
I used my calculator to find x = appr. 2170 days
so the father is 2170/30 or 72 yrs
the son is 2170/52 or 42 yrs
grandson is 2170/365 or 6 years
The previous was my solution, should have said Reiny instead of Anonymous
let the age of the grandson be x days
so the age of the son is x weeks
and the age of the father is x/30 years
so,...
Grandson = x days = x/30 months = x/365 years
Son = x weeks = x/5s years
father = x/30 years
then x/30 + x/52 + x/365 = 120
x(1/30 + 1/52 + 1/365) = 120
I used my calculator to find x = appr. 2170 days
so the father is 2170/30 or 72 yrs
the son is 2170/52 or 42 yrs
grandson is 2170/365 or 6 years
To solve this problem, let's define the ages of the grandson, the son, and the father as follows:
Let G be the age of the grandson in years.
Let S be the age of the son in years.
Let F be the age of the father in years.
Now, let's translate the information given into equations:
1. "The grandson is about as many days old as the son is in weeks":
This means that the age of the grandson in days is approximately the age of the son in weeks, or G * 365 ≈ S * 52.
2. "The grandson is approximately as many months old as the father is in years":
This means that the age of the grandson in months is approximately the age of the father in years, or G * 12 ≈ F.
3. "The ages of the grandson, the son, and the father add up to 120 years":
This can be written as G + S + F = 120.
Now, let's solve these equations simultaneously. We'll start by rearranging equation 1 to solve for S:
S ≈ (G * 365) / 52.
Next, let's rearrange equation 2 to solve for F:
F ≈ G * 12.
Now, substitute these expressions for S and F into equation 3:
G + (G * 365) / 52 + G * 12 = 120.
To simplify this equation, we can multiply all terms by 52 to get rid of the denominator:
52G + 365G + 52 * 12G = 120 * 52.
Combine like terms:
429G = 6240.
Solve for G:
G = 6240 / 429 ≈ 14.52 (rounded to two decimal places).
Now, substitute this value for G back into equation 1 to find S:
S ≈ (14.52 * 365) / 52 ≈ 102 (rounded to the nearest whole number).
Finally, substitute the values for G and S back into equation 3 to find F:
F = 120 - (G + S) ≈ 120 - (14.52 + 102) = 3.48 (rounded to two decimal places).
Therefore, the ages of the grandson, son, and father in years are approximately 14.52, 102, and 3.48, respectively.