To solve this problem, let's assign variables to the ages of the grandson, son, and yourself.
Let:
- $g$ be the age of the grandson in years
- $s$ be the age of the son in years
- $y$ be your age in years
From the given information, we have three equations:
The grandson is about as many days old as the son is weeks old:
$g = 7s$
The grandson is as many months old as you are years old:
$g = 12y$
The sum of the ages of the grandson, son, and yourself is 100 years:
$g + s + y = 100$
Now, let's solve these equations to find the values of $g$, $s$, and $y$.
From equation (1), we can substitute $g$ in equation (3):
$7s + s + y = 100$
Simplifying this equation gives:
$8s + y = 100$
From equation (2), we can substitute $g$ in equation (3):
$12y + s + y = 100$
Simplifying this equation gives:
$s + 13y = 100$
We now have a system of two linear equations with two variables. We can solve this system using substitution or elimination. Let's use the substitution method.
From equation (8), we can isolate $s$:
$s = 100 - 13y$
Substituting this value of $s$ into equation (7):
$8(100 - 13y) + y = 100$
Expanding and simplifying this equation gives:
$800 - 104y + y = 100$
Combining like terms:
$-103y = -700$
Dividing both sides by $-103$:
$y = \frac{-700}{-103} = \frac{700}{103}$
So your age in years is approximately $\frac{700}{103}$. To find the closest whole number, we can divide 700 by 103 and round the result to the nearest whole number.
Using long division, we find:
$700 \div 103 \approx 6$
Therefore, your age in years is approximately 6.
The correct answer is A) 60.