SOLUTION: a woman is three times as old as her daughter was at the time when the mother was twice as old as her daughter will be two years from now. find the current age of each if the sum

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Question 786274: a woman is three times as old as her daughter was at the time when the mother was twice as old as her daughter will be two years from now. find the current age of each if the sum of their ages is 55
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = mother's age now
Let +d+ = daughter's age now
----------------------------
+d+%2B+2+ = daughter's age +2+ yrs from now
+2%2A%28+d+%2B+2+%29+ = twice daughter's age +2+ yrs from now
----------------------------
+m+%2B+d+=+55+
+-d+=+m+-+55+
+m+-+d+=+m+%2B+m+-+55+
+m+-+d+=+2m+-+55+
The difference in their ages will always be +55+ yrs
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When the mother was +2%2A%28+d+%2B+2+%29+, the daughter
was +2%2A%28+d+%2B+2+%29+-+%28+2m+-+55+%29+
also given:
+m+=+3%2A%28+2%2A%28+d%2B2+%29+-+%28+2m+-+55+%29+%29+
+m+=+3%2A%28+2d+%2B+4+-+2m+%2B+55+%29+
+m+=+3%2A%28+2d+-+2m+%2B+59+%29+
+m+=+6d+-+6m+%2B+177+
+7m+=+6d+%2B+177+
and, since +m+%2B+d+=+55+,
+7m+=+6%2A%28+55+-+m+%29+%2B+177+
+7m+=+330+-+6m+%2B+177+
+13m+=+507+
+m+=+39+
and
+d+=+55+-+m+
+d+=+16+
The woman is 39 and the daughter is 16
check:
2 yrs from now, daughter is 18
twice that is 36
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When the mother was 36, daughter was 13
Three time 13 is 39
OK