SOLUTION: john is twice jane’s age. in 2 year’s time, john will be twice as old as jill and she will be twice as old as jane’s age 2 years ago. how old are john, jill and jane?

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Question 921649: john is twice jane’s age. in 2 year’s time, john will be twice as old as jill and she will be twice as old as jane’s age 2 years ago. how old are john, jill and jane?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = John's age now
Let +b+ = Jill's age now
Let +c+ = Jane's age now
---------------------------
(1) +a+=+2c+
(2) +a+%2B+2+=+2%2A%28+b+%2B+2+%29+
(3) +b+%2B+2+=+2%2A%28+c+-+2+%29+
-------------------------
(2) +a+%2B+2+=+2b+%2B+4+
(2) +a+-+2b+=+2+
and
(3) +b+%2B+2+=+2c+-+4+
(3) +-b+%2B+2c+=+6+
---------------------
(1) +c+=+%281%2F2%29%2Aa+
Substitute (1) into (3)
(3) +-b+%2B+2c+=+6+
(3) +2%2A%281%2F2%29%2Aa+-+b+=+6+
(3) +a+-+b+=+6+
Subtract (2) from (3)
(3) +a+-+b+=+6+
(2) +-a+%2B+2b+=+-2+
---------------------
+b+=+4+
and
(3) +a+-+b+=+6+
(3) +a+-+4+=+6+
(3) +a+=+10+
and
(1) +c+=+%281%2F2%29%2Aa+
(1) +c+=+5+
---------------
John is 10
Jill is a 4
Jane is 5
-----------
check:
John is twice Jane's age -OK
In 2 year’s time, john will be twice as old as jill
True- John will be 12 and Jill will be 6
Jill will be twice as old as jane’s age 2 years ago
True- Jane was 3 and Jill will be 6
OK