SOLUTION: Sam is 6 years older than Jane. 6 years ago he was twice as old as Jane was. How old is Jane now?

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Question 1044843: Sam is 6 years older than Jane. 6 years ago he was twice as old as Jane was. How old is Jane now?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Jane's age now
Let +b+ = Sam's age now
+a+-+6+ = Sam's age 6 yrs ago
+b+-+6+ = Jane's age 6 yrs ago
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(1) +a+=+b+%2B+6+
(2) +a+-+6+=+2%2A%28+b+-+6+%29+
-----------------------
(1) +a+-+b+=+6+
(2) +a+-+6+=+2b+-+12+
(2) +-a+%2B+2b+=+6+
-----------------------
Add (1) and (2)
(1) +a+-+b+=+6+
(2) +-a+%2B+2b+=+6+
--------------------
+b+=+12+
and
(1) +a+-+b+=+6+
(1) +a+-+12+=+6+
(1) +a+=+18+
-------------------
Jane is 18 now
-------------------
check:
(1) +a+=+b+%2B+6+
(1) +18+=+12+%2B+6+
(1) +18+=+18+
and
(2) +a+-+6+=+2%2A%28+b+-+6+%29+
(2) +18+-+6+=+2%2A%28+12+-+6+%29+
(2) +12+=+2%2A6+
(2) +12+=+12+
OK

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The age difference is always 6 years.
----
Twice as old --> 6 & 12
etc.