SOLUTION: Ann is 6 years older than Mary. She is also twice as old as Mary was when Ann was as old as Mary is now. How old is each now?

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Question 108127: Ann is 6 years older than Mary. She is also twice as old as Mary was when Ann was as old as Mary is now. How old is each now?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If Ann=x-years-old =>
And Mary=y-years-old
Then:
x+=+y%2B6...because Ann is 6 years older than Mary.
and
x=2y-6....She is also twice as old as Mary was when Ann-+was-+as+-old-+as-+Mary-+is+-now

use these two equations above to solve the problem:

since the left sides of the equations above are equal, and then right sides must be equal too:
y%2B6+=+2y-6
y+%2B+6+=+2y-6+….move y+
6+%2B6=+2y-y
y+=+12……….. Mary is12-years-old
Then ………………......Ann is 18-years-old

check:
Ann is 18, Mary is 12 => Ann is 6 years older then Mary or12+%2B6=18
When Ann was as old as Mary is now, means it was before 6
years
and before 6 years Ann was 18-6=12 and Mary was 12-6+=+6
When Ann was 12, she was twice as old as Mary (2%2A6=12).