SOLUTION: Maria is now 3 years younger than her sister, Ann. Four years ago, Maria’s age was one-half Anna’s age. How old is each girl now?

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Question 1012091: Maria is now 3 years younger than her sister, Ann. Four years ago, Maria’s age was one-half Anna’s age. How old is each girl now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = Maria's age now
Let +a+ = Anna's age now
-------------------------
given:
(1) +m+=+a+-+3+
(2) +m+-+4+=+%28+1%2F2+%29%2A%28+a+-+4+%29+
---------------------------
I will substitute (1) into (2)
(2) +a+-+3+-+4+=+%28+1%2F2+%29%2A%28+a+-+4+%29+
(2) +a+-+7+=+%281%2F2%29%2A%28+a+-+4+%29+
(2) +2%28+a+-+7+%29+=+a+-+4+
(2) +2a+-+14+=+a+-+4+
(2) +a+=+14+-+4+
(2) +a+=+10+
and
(1) +m+=+a+-+3+
(1) +m+=+10+-+3+
(1) +m+=+7+
-----------------
Maria is 7 and Anna is 10
check:
(2) +m+-+4+=+%28+1%2F2+%29%2A%28+a+-+4+%29+
(2) +7+-+4+=+%28+1%2F2+%29%2A%28+10+-+4+%29+
(2) +3+=+%281%2F2%29%2A6+
(2) +6+=+6+
and
(1) +m+=+a+-+3+
(1) +7+=+10+-+3+
(1) +7+=+7+
OK