SOLUTION: Melissa is 24 years younger than Joyce. In 2 years, Joyce will be 3 times as old as Melissa will be then. How old are they now?

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Question 1051263: Melissa is 24 years younger than Joyce. In 2 years, Joyce will be 3 times as old as Melissa will be then. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Melissa's age now
Let +b+ = Joyce's age now
-----------------------------
(1) +a+=+b+-+24+
(2) +b+%2B+2+=+3%2A%28+a+%2B+2+%29+
---------------------------
(2) +b+%2B+2+=+3a+%2B+6+
(2) +-3a+%2B+b+=+4+
and
(1) +-a+%2B+b+=+24+
-------------------------
Subtract (2) from (1)
(1) +-a+%2B+b+=+24+
(2) +3a+-+b+=+-4+
---------------------
+2a+=+20+
+a+=+10+
and
(1) +-a+%2B+b+=+24+
(1) +-10+%2B+b+=+24+
(1) +b+=+34+
-----------------------
Joyce is 34
Melissa is 10
---------------
check:
(1) +a+=+b+-+24+
(1) +10+=+34+-+24+
(1) +10+=+10+
and
(2) +b+%2B+2+=+3%2A%28+a+%2B+2+%29+
(2) +34+%2B+2+=+3%2A%28+10+%2B+2+%29+
(2) +36+=+3%2A12+
(2) +36+=+36+
OK