SOLUTION: Joy is 10 years older than EJ. Five years ago, EJ is 1/3 as old as Joy. What are their present ages?

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Question 1149870: Joy is 10 years older than EJ. Five years ago, EJ is 1/3 as old as Joy. What are their present ages?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = EJ's age now
+x+%2B+10+ = Joy's age now
-----------------------------------
+x+-+5+=+%28+1%2F3+%29%2A%28+x+%2B+10+-+5+%29+
+3%2A%28+x+-+5+%29+=+x+%2B+5+
+3x+-+15+=+x+%2B+5+
+2x+=+20+
+x+=+10+
and
+x+%2B+10+=+20+
-----------------------
EJ is 10
Joy is 20
----------------
check answer:
5 yrs ago,
EJ is 5
Joy is 15
------------
+5+=+%281%2F3%29%2A15+
+5+=+5+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


With logical reasoning instead of formal algebra....

The difference in their ages is 10 years; when EJ was 1/3 as old as Joy, their ages had to be 5 and 15.

That was 5 years ago, so their ages now are 10 and 20.