SOLUTION: Separate 54 into two parts such that 1/12 of the difference between them is 1/3.

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Question 937146: Separate 54 into two parts such that 1/12 of the difference between them is 1/3.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ be one part and
+54+-+x+ be the other part
+%28+1%2F12+%29%2A%28+x+-+%28+54+-+x+%29+%29+=+1%2F3+
Multiply both sides by +12+
+x+-+%28+54++-+x+%29+=+4+
+x+-+54+%2B+x+=+4+
+2x+=+58+
+x+=+29+
and
+54+-+x+=+54+-+29+
+54+-+x+=+25+
----------------
The parts are 29 and 25
check:
+%28+1%2F12+%29%2A%28+x+-+%28+54+-+x+%29+%29+=+1%2F3+
+%28+1%2F12+%29%2A%28+29+-+25+%29+=+1%2F3+
+%28+1%2F12+%29%2A4+=+1%2F3+
+1%2F3+=+1%2F3+
OK