Let f represent Frank's age. Let s represent his sister's age.

Frank is eight years older than his sister.

So f = s + 8.

In three years Frank will be twice as old as his sister will be.

So f +3 = 2(s + 3).

Now substitute the value of f into the equation and solve for s.

s + 8 + 3 = 2(s + 3)

s + 11 = 2s +6

11 = s + 6

5 = s

Since the sister's age is 5 then Frank's age is 13.