In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 25years time I shall only be twiceher age." How old are the man and the woman?

Let the age of the man (in years) be [tex]y_{man}[/tex] and the age of the woman (in years) be [tex]y_{woman}[/tex], right now he is three times her age, so:

[tex]y_{man} \ = \ 3 \ y_{woman}[/tex]

We also know that in 25 years, his age, [tex]y_{man25}[/tex], will be two times the age of hers, [tex]y_{woman25}[/tex], so:

[tex]y_{man25} \ = \ 2 \ y_{woman25}[/tex].

Now, of course, the age of each one, in 25 years, will be the same age they got right now plus 25 years;

[tex]y_{man25} \ = y_{man} + 25[/tex]

[tex]y_{woman25} \ = y_{woman} + 25[/tex]

We can replace this values on our second equation, and get:

[tex]y_{man} + 25 \ = \ 2 \ (y_{woman} + 25)[/tex]

Working it a little:

[tex]y_{man} \ = \ 2 \ y_{woman} + 2* 25 - 25[/tex]

[tex]y_{man} \ = \ 2 \ y_{woman} + 50 - 25[/tex]

[tex]y_{man} \ = \ 2 \ y_{woman} + 25[/tex]

We can replace this value on our first equation:

[tex]\ 2 \ y_{woman} + 25 \ = \ 3 \ y_{woman}[/tex]

[tex] 25 \ = \ 3 \ y_{woman} - \ 2 \ y_{woman} [/tex]

[tex] 25 \ = (\ 3 \ - \ 2\ ) y_{woman} [/tex]

[tex] 25 \ = y_{woman} [/tex]

The woman its 25 years old! We know the man its three times that age, so:

[tex] y_{man} = 3* 25 = 75 [/tex].

The man its 75 years old!

In 25 years she will be 50 and he will be 100, exactly two times her age. :)

In a​ film, a character is criticized for marrying a woman when he is three times her age. He wittily​ replies, "Ah, but in 25years time I shall only be twiceher​ age." How old are the man and the​ woman?

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In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 25years time I shall only be twiceher age." How old are the man and the woman?