SOLUTION: Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?

Let y be Evan's age, and

let x be the sister's age.



From the condition, you have these two equations

y - 3 = ,      (1)    ("Three years ago, Evan was one third of his sister's age.")

2*(y+1) = x + 1.      (2)     ("In a year's time, Evan's age doubled will match his sister's age.")



From eq(1),  3*(y-3) = x - 3  ====>  3y - 9 = x - 3  ====>  x = 3y - 6.

Now substitute it into eq(2). You will get

2*(y+1) = (3y-6) + 1  ====>  2y + 2 = 3y - 5  ====>  y = 2 + 5 = 7.



Answer.  Evan is 7 years old.  His sister is 15 years old (from eq(2)).