In a film, actor Charles Coburn plays an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. He wittily replies, "Ah, but in 30 years time I shall only be twice her age." Using algebra as opposed to "trial & error", how old is the "uncle" and the woman?

Each answer must be explained in detail using the correct vocabulary to receive full credit.

Age of uncle = 90 years

Age of woman = 30 years

Step-by-step explanation:

Let the age of uncle be x years

And age of woman be y years

Now, uncle is three times her age ⇒ x = 3y ... (1)

Also, in 30 years uncle is twice her age ⇒ x + 30 = 2 (y + 30) ... (2)

Now, substituting x = 3y from equation (1) in equation (2)

⇒ 3y + 30 = 2y + 60

⇒ y = 30

So, x = 90

Hence, Age of uncle = 90 years

Age of woman = 30 years