SOLUTION: Paula is 12 years older than her brother Bob.Four years from now Bob will be two thirds as old as Paula. how old are they now ?

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Question 658385: Paula is 12 years older than her brother Bob.Four years from now Bob will be two thirds as old as Paula. how old are they now ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = Paula's age now
Let +b+ = Bob's age now
given:
(1) +p+=+b+%2B+12+
(2) +b+%2B+4+=+%282%2F3%29%2A%28+p+%2B+4+%29+
---------------------------
(2) +3b+%2B+12+=+2p+%2B+8+
(2) +2p+-+3b+=+4+
Substitute (1) into (2)
(2) +2%2A%28+b+%2B+12+%29+-+3b+=+4+
(2) +2b+%2B+24+-+3b+=+4+
(2) +-b+=+-20+
(2) +b+=+20+
and
(1) +p+=+b+%2B+12+
(1) +p+=+20+%2B+12+
(1) +p+=+32+
Paula is 32
Bob is 20
------------
check:
In 4 years Paula is 36
In 4 years Bob is 24
+24+=+%282%2F3%29%2A36+
Divide both sides by 12
+2+=+%282%2F3%29%2A3+
+2%2F3+=+2%2F3+
OK