SOLUTION: The sum of a man's age and his sisters age is 91. The man is twice as old as his sister was when the man was as old as his sister is today. How old are they?

Question 697171: The sum of a man's age and his sisters age is 91. The man is twice as old as his sister was when the man was as old as his sister is today. How old are they?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the Man's age now
Let = his Sister's age now
given:
(1)
When the Man's age was , the age his
Sister is now, how old was his Sister then?
--------------
The separation in their ages will always be

( assuming the Man is older )
So, when the Man was years old, his Sister
was

---------------------
The man is now twice this age, so he is

And, I can now say

Substitute this into (1)
(1)
(1)
(1)
(1)
(1)
and, since
(1)
(1)
(1)
(1)
The man is 52
His Sister is 39
---------
check:
52 - 39 = 13, which is always
the difference in their ages
When the man was 39 , his Sister was 39 - 13 = 26
The Man is twice this age, or 2*26 = 52
OK

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