Discovering ages

I HAVE THE AGE OF DOUBLE WHAT you had WHEN I WAS YOUR AGE. If thou MY AGE, THE SUM OF OUR AGE WILL BE 45 YEARS. WHAT ARE OUR AGES ???


SOLUTION: Only read after trying to solve!

You had an age which we call the x and today HAS an age which we will call y.

I HAVE twice the age that you had when I was your current age y (double x), ie I HAVE 2x years.

THEN:

You had x and y now has.
I HAD y and I now have 2x.

So we have:

y = 2x-x-y

2y = 3x

x = (2/3) * y

SO substituting the value of x, we have:

You had (2/3) * ye now has y.Eu HAD ye now have (4/3) * y.

Now pay attention to the second sentence:

If thou MY AGE, THE SUM OF OUR AGE WILL BE 45 YEARS.

You have y, and to have my age, which is (4/3) * y, must be added to your age y more (1/3) * y.

Adding y + (1/3) * y you will have my age, that is, you will have (4/3) * y.

As we add (1/3) * y to their age, we must add to my well, ie:

Now I have (4/3) * y + (1/3) * y, then I have (5/3) * y.

The sum of our ages should be equal to 45:

(4/3) * y + (5/3) * y = 45

(9/3) * y = 45

3y = 45

y = 15

Earlier we found that x = (2/3) * y thus x = (2/3) * 15, then x = 10.

FINALLY: WHAT ARE OUR AGES ???

AS SAID EARLIER, YOUR CURRENT AGE IS y, THAT IS 15 YEARS.

AND MY AGE IS 2x, IE 2.10, THAT IS EQUAL TO 20 YEARS.

SO THE AGES ARE 20 AND 15 YEARS !!!