Question

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?

Answer 1

Answer:

The woman its 25 years old. The man its 50.

Step-by-step explanation:

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

$y_{man} \ = \ 3 \ y_{woman}$

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

$y_{man25} \ = \ 2 \ y_{woman25}$.

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

$y_{man25} \ = y_{man} + 25$

$y_{woman25} \ = y_{woman} + 25$

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

$y_{man} + 25 \ = \ 2 \ (y_{woman} + 25)$

Working it a little:

$y_{man} \ = \ 2 \ y_{woman} + 2* 25 - 25$

$y_{man} \ = \ 2 \ y_{woman} + 50 - 25$

$y_{man} \ = \ 2 \ y_{woman} + 25$

We can replace this value on our first equation:

$\ 2 \ y_{woman} + 25 \ = \ 3 \ y_{woman}$

$25 \ = \ 3 \ y_{woman} - \ 2 \ y_{woman}$

$25 \ = (\ 3 \ - \ 2\ ) y_{woman}$

$25 \ = y_{woman}$

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

$y_{man} = 3* 25 = 75$.

The man its 75 years old!

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

Answer 2

Answer:age of the man: 75 age of the woman:25

Step-by-step explanation:

First, We need to define the variables

x: age of the man

y: age of the woman

at the first time he has three times her age

x=3y                (1)

in 25 years time

(x+25)=2(y+25)                 (2)

we clear the equation

X+25=2y+50

X=2y+25

we substitute in the (1) equation:

2y+25=3y

y=25

x=3*25=75