1. ## Age Comparison Challenge

Hey, everyone. I have a problem for you to solve. I tried but don't know how to complete it. Here is the problem:

"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 are 140 years. Can you tell me my age in years?"

So that's what the problem said. If there are any answers, I'll gladly accept them. Thanks in advance!

2. Hello, Dried Monkey!

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 total 140 years.
Can you tell me my age in years?

Let: .$\displaystyle \begin{array}{ccc}G &=& \text{Grandson's age in years} \\ S &=& \text{Son's age in years} \\ M &= & \text{My age in years} \end{array}$

Let's take each sentence separately.

"My grandson is about as many days as my son is weeks."
My son's age in days is seven times my grandson's age in days.
That is, my son is seven times older than my grandson: .$\displaystyle S \:=\:7G$

"And my grandson is as many months as I am in years."
My grandson is $\displaystyle G$ years old; that is, he is $\displaystyle 12G$ months old.
Hence, we have: .$\displaystyle 12G \:=\:M$

"My grandson, my son, and I total 140 years": .$\displaystyle G + S + M \:=\:140$

We have a system of equations: .$\displaystyle \begin{array}{cccc} 7G - S &=& 0 & [1] \\ 12G - M &=& 0 & [2] \\ G + S + M &=&140 & [3] \end{array}$

$\displaystyle \begin{array}{cccc}\text{Add [2] and [3]:} & 13G + S &=& 140 \\ \text{Add [1]:} & 7G - S &=& 0 \end{array}$

And we have: .$\displaystyle 20G \:=\:140\quad\Rightarrow\quad G \:=\:7$

Substitute into [1]: .$\displaystyle 7(7) - S \:=\:0 \quad\Rightarrow\quad S \:=\:49$

Substitute into [2]: .$\displaystyle 12(7) - M \:=\:0 \quad\Rightarrow\quad M \:=\:84$

Therefore, my grandson is 7, my son is 49, and I am 84.

3. Originally Posted by Dried Monkey
Hey, everyone. I have a problem for you to solve. I tried but don't know how to complete it. Here is the problem:

"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 are 140 years. Can you tell me my age in years?"

So that's what the problem said. If there are any answers, I'll gladly accept them. Thanks in advance!
Since the number of days in a month varies, you have to round a bit.

X (days) = Y (weeks) => X = Y.

X/30 (months) = Z (years) => X = 30 Z.

$\displaystyle \frac{X}{364} + \frac{Y}{52} + Z = 140$.

I get Z = 84 years.