SOLUTION: John is 5 years older than Mary. In 10 years, twice john's age decreased by Mary's age is 35, and john's age will be twice Mary's current age. Find their current ages now.

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: John is 5 years older than Mary. In 10 years, twice john's age decreased by Mary's age is 35, and john's age will be twice Mary's current age. Find their current ages now.      Log On

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Question 624880: John is 5 years older than Mary. In 10 years, twice john's age decreased by Mary's age is 35, and john's age will be twice Mary's current age. Find their current ages now.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = John's age now
Let +m+ - Mary's age now
given:
(1) +j+=+m+%2B+5+
(2) +2%2A%28+j+%2B+10+%29+-+%28+m+%2B+10+%29+=+35+
(3) +j+%2B+10+=+2m+
------------------
(3) +j+=+2m+-+10+
Substitute this into (1)
(1) +2m+-+10+=+m+%2B+5+
(1) +m+=+15+
and
(1) +j+=+m+%2B+5+
(1) +j+=+15+%2B+5+
(1) +j+=+20+
------------
Now (2) must also be true
(2) +2%2A%28+j+%2B+10+%29+-+%28+m+%2B+10+%29+=+35+
(2) +2%2A%28+20+%2B+10+%29+-+%28+15+%2B+10+%29+=+35+
(2) +2%2A30+-+25+=+35+
(2) +60+-+25+=+35+
(2) +35+=+35+
OK
Currently, Mary is 15 and John is 20