SOLUTION: I am twice as old as she was when I was as old as she is. when she is as old as I am now, the sum of our ages will be 63

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Question 505755: I am twice as old as she was when I was as old as she is. when she is as old as I am now, the sum of our ages will be 63
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


What a fascinating little tidbit of information. Did you have a question to ask?

John

My calculator said it, I believe it, that settles it
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I guess the question is " How old are they now?"
Let a = my age now
Let b = her age now
given:
The difference in their ages is always +a+-+b+
When I was b years old, how old was she?
She was +b+-+%28+a+-+b+%29++=+2b+-+a+ yrs old
Now I am twice this age, or +4b+-+2a+, so
+a+=+4b+-+2a+
(1) +3a+=+4b+
------------
When she is a yrs old, I will be +a+%2B+%28+a+-+b+%29+=+2a+-+b+
The sum of our ages is 63, so
+a+%2B+2a+-+b+=+63+
(2) +3a+-+b+=+63+
Substitute (1) into (2)
(2) +4b+-+b+=+63+
(2) +3b+=+63+
(2) +b+=+21+
and, since
(1) +3a+=+4b+
(1) +a+=+4%2A21%2F+3
(1) +a+=+28+
I am 28 and she is 21
check answer:
When I was 21, she was 21 - (28 - 21) = 14
I am twice this age, or 28
----------------------
When she is as old as I am now, or 28, that will be in 28 - 21 = 7 years
and I will be 28 + 7 = 35, and the sum of our ages will be 28 + 35 = 63
OK