Frank is 13 and his sister is 5.

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.

 

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