A man and a woman have the same birthday. When he was as old as she is now, the man was twice as old as the woman. When she becomes as old as he is now, the sum of their ages will be 119. Let x be the man’s age now. How old are the man and the woman now?

Answer: The man is 51 years old, and the woman is 34 years old.

Step-by-step explanation:

x is the age of the man now

Let y be the age of the woman now.

When the man was y years old, the woman was y/2 years old, and their age difference was

y - y/2 = y/2

Their age difference remains the same, so, their age difference now is y/2

That is

x - y = y/2

x = (3/2) y

When the woman is the current age of the man (x years), the man's age is increase by y/2 (x + y/2), and the sum of their ages is 119

x + x + y/2 = 119

2x + y/2 = 119

But x = (3/2) y

So

2 (3/2) y + y/2 = 119

3y + y/2 = 119

Multiply through by 2

6y + y = 238

7y = 238

y = 34

We know x = (3/2) y

x = (3/2) * 34

= 51

Therefore, the man's age, x, is 51 years, and the woman's age, y, is 34 years.