SOLUTION: 5 yrs ago Ben was 2/3 as old as Kris. 10 yrs from now he will be 5/6 as old as Kris. how old are they now.

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Question 772280: 5 yrs ago Ben was 2/3 as old as Kris. 10 yrs from now he will be 5/6 as old as Kris. how old are they now.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = Ben's age now
Let +k+ = Kris's age now
-----------------------
(1) +b+-+5+=+%282%2F3%29%2A%28+k+-+5+%29+
(2) +b+%2B+10+=+%285%2F6%29%2A%28+k+%2B+10+%29+
-----------------------------
(1) +3%2A%28+b+-+5+%29+=+2%2A%28+k+-+5+%29+
(1) +3b+-+15+=+2k+-+10+
(1) +3b+-+2k+=+5+
and
(2) +6%2A%28+b+%2B+10+%29+=+5%2A%28+k+%2B+10+%29+
(2) +6b+%2B+60+=+5k+%2B+50+
(2) +6b+-+5k+=+-10+
--------------------
Multiply both sides of (1) by +2+
and subtract (2) from (1)
(1) +6b+-+4k+=+10+
(2) +-6b+%2B+5k+=+10+
+k+=+20+
and, since
(1) +3b+-+2k+=+5+
(1) +3b+-+2%2A20+=+5+
(1) +3b+=+45+
(1) +b+=+15+
Ben is 15 and Kris is 20
check:
(1) +b+-+5+=+%282%2F3%29%2A%28+k+-+5+%29+
(1) +15+-+5+=+%282%2F3%29%2A%28+20+-+5+%29+
(1) +10+=+%282%2F3%29%2A15+
(1) +30+=+2%2A15+
(1) +30+=+30+
OK -you can check other equation