My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?

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:

1. The grandson is about as many days old as the son is weeks old: $g = 7s$

2. The grandson is as many months old as you are years old: $g = 12y$

3. 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.

• Thanks
• Wrong explanation