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

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

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

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