How do I solve this?

[volvo179]

"My friend and I have a combined age of 91 years. I am twice as old as my friend was when I was as old as he is now""


What are our ages now?

[kissingdog]

I'm not sure how I solved it but the ages now are 39 and 52. There is 13 years between them so 13 years ago his friend was 26.

[crofter]

volvo179 Do you still want the solution?

Let my age be x and my (younger) friend's be y. Hence the first (and easy) equation is x + y = 91. The next equation is not so easy but (x - y) years ago I was aged x - ( x - y) = y years and my friend was aged y - (x - y) years, which is the same as (2y - x) years (Are still following this?)

The second equation now is "my current age (x) is TWICE this (2y - x) age", so x = 2(2y - x). This can be simplified to x = 4y - 2x or better 3x = 4y.

Now SOLVING x + y = 91 and 3x = 4y, we begin by scaling up the first equation by 3 to get 3x + 3y = 273

Substituting from the second equation, we arrive at the result 4y + 3y = 7y = 273 , and so y = 39 years.

Hence x = 91 - y = 91 - 39 = 52 years, as given by kissingdog.

[volvo179]

Thank you Kissingdog and Crofter. I had been struggling with this for hours!!