Answer :
Let m be my age in years.
If s is my son's age in years, then my son is 52s weeks old. If g is my
grandson's age in years, then my grandson is 365g days old. Thus,
365g = 52s.
Since my grandson
is 12g months old,
12g = m.
Since my grandson,
my son and I together are 120 years,
g + s + m = 120.
The above system of
3 equations in 3 unknowns (g, s and m) can be solved as follows.
m / 12 + 365 m /
(52 x 12) + m = 120 or
52 m + 365 m + 624
m = 624 x 120 or
m = 624 x 120 /
1041 = 72.
So, I am 72 years
old.
The problem is hard...i don't know if you understood this..Hope i helped!
x - your son's age in years
y - your age in years
There are 52 weeks in a year and 365 days in a year, so the age of your grandson in years is (52x)/365
There are 12 months in a year, so the age of your grandson in years is y/12.
Set both expressions equal to each other:
[tex]\frac{52x}{365}=\frac{y}{12} \\ 52x \times 12=365y \\ 624x=365y \\ x=\frac{365}{624}y[/tex]
Your son's age is equal to 365/624 of your age.
Your grandson, your son and you together are 120 years.
[tex]\frac{1}{12}y+\frac{365}{624}y+y=120 \\ \frac{52}{624}y+\frac{365}{624}y+\frac{624}{624}y=120 \\ \frac{1041}{624}y=120 \\ y=120 \times \frac{624}{1041} \\ y \approx 72[/tex]
You are 72 years old.
y - your age in years
There are 52 weeks in a year and 365 days in a year, so the age of your grandson in years is (52x)/365
There are 12 months in a year, so the age of your grandson in years is y/12.
Set both expressions equal to each other:
[tex]\frac{52x}{365}=\frac{y}{12} \\ 52x \times 12=365y \\ 624x=365y \\ x=\frac{365}{624}y[/tex]
Your son's age is equal to 365/624 of your age.
Your grandson, your son and you together are 120 years.
[tex]\frac{1}{12}y+\frac{365}{624}y+y=120 \\ \frac{52}{624}y+\frac{365}{624}y+\frac{624}{624}y=120 \\ \frac{1041}{624}y=120 \\ y=120 \times \frac{624}{1041} \\ y \approx 72[/tex]
You are 72 years old.
