SOLUTION: Marie is one-nineth as old as her mother. In 3 years she will be one-fifth as old as her mother will be then. Find their present ages.

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Question 268953: Marie is one-nineth as old as her mother. In 3 years she will be one-fifth as old as her mother will be then. Find their present ages.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
(i) Ma+=+%281%2F9%29Mo
(ii)+%28ma+%2B+3%29+=+%281%2F5%29%2A%28mo+%2B+3%29
from (i) we get
(iii) 9ma+=+Mo
substitute this into (ii) we get
(iv) %28ma+%2B+3%29+=+%281%2F5%29%2A%289ma+%2B+3%29
distribute to get
(v) %28ma+%2B+3%29+=+%289%2F5%29%2Ama+%2B+3%2F5%29
subtract ma and subtract 3/5 to get
(vi) 12%2F5+=+%284%2F5%29ma
multiply by 5 to get
(vii) 12+=+4ma
divide by 4 to get
maria = 3
mother = 27