SOLUTION: Millie is 2/3 as old as maude. Six years from now millie will be 5/7 as old as maude will be. How old is each?

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Question 130578: Millie is 2/3 as old as maude. Six years from now millie will be 5/7 as old as maude will be. How old is each?
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
MILLIE=2X/3 NOW.
MAUDE=X NOW.
IN 6 YEARS:
(2X/3)+6=5/7(X+6)
2X/3+6=(5X+30)/7 CROSS MULTIPLY
5X+30=7(2X/3+6)
5X+30=14X/3+42
5X+30=(14X+3*42)/3
5X+30=(14X+126)/3 CROSS MULTIPLY
3(5X+30)=14X+126
15X-14X=126-90
X=36 MAUDE'S AGE NOW.
2*36/3=72/3=24 MILLIE'S AGE NOW.
PROOF
24+6=(5/7)(36+6)
30=(5*42/7)
30=210/7
30=30