Question

A grandmother is now 48 years older than her grandson. 14 years ago she was thirteen times as old as her grandson. How old is the grandmother? How old is the grandson?

Answer 1

Let's call the grandmother's current age G and the grandson's current age S.

From the first piece of information given, we know that:

G = S + 48

From the second piece of information given, we know that:

G - 14 = 13S

We can use the first equation to substitute for G in the second equation:

(S + 48) - 14 = 13S

S + 34 = 13S

34 = 12S

S = 34/12

S = 2.8 years

So the grandson is 2.8 years old.

Now we can use this information to find the grandmother's age:

G = S + 48

G = 2.8 + 48

G = 50.8 years

So, the grandmother is 50.8 years old and the grandson is 2.8 years old.