To my Grandpa

Let's take the value of my age as $x$ . Therefore my age seven years ago was $x-7$ .

According to the question, my grandpa's age was $8(x-7)=8x-56$ .

But, $\dfrac{x}{8x-56}=\dfrac{1}{4}$

Or, $8x-56=4x$

Or, $4x=56$ I.e, $x=14$

Therefore my grandpa's age, seven years ago $=8(14)-56=112-56=56$

Hence my grandpa's age $=56+7=63$

Therefore my age + my grandpa's age $= 63+14=\boxed{77}$

Note: the values of the ages mentioned are true real life values . . . . . .

My current (unknown) age = x

My age seven years ago = x - 7

My younger self = 8(x-7) = GP (grandpa) seven years ago

My older self = 4x = GP seven years ago

8(x-7) = 4x

8x - 56 = 4x

8x - 4x = 56

x = 14

Therefore, seven years ago, I was (14 - 7), and GP = 56

Today, GP = 56 + 7 = 63

63 + 14 = 77

Let $A$ be the present age of your grandpa and $B$ be your present age. We have our first equation,

$A-7=8(B-7)=8B-56$ $\implies$ $A=8B-49$ $\color{#D61F06}(1)$

Then our second equation would be

$\dfrac{B}{A-7}=\dfrac{1}{4}$ $\implies$ $4B=A-7$ $\color{#D61F06}(2)$

Substitituting $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$4B = 8B - 49 - 7$

$-4B = -56$

$B=14$

It follows that $A=8(14)-49 = 63$

The desired answer is $14+49 = \boxed{77}$

It shows that you love your grandpa that much. Maybe you have many unforgettable memories.