SOLUTION: MATH QUESTION--- A man bought some articles for $540. He lost 2 and sold the rest at $6 per article more than he gave for them. On the whole transaction he gained 10% on his outla

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Question 758664: MATH QUESTION---
A man bought some articles for $540. He lost 2 and sold the rest at $6 per article more than he gave for them. On the whole transaction he gained 10% on his outlay. How many articles did he buy?
Please help!
Thank You for Your Time :D

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of articles he bought
+540%2Fn+ = the cost / article that he bought
He lost 2, so he had +n+-+2+ left
He sold the rest at $6 per article more than he gave for them
+540%2Fn+%2B+6+ per item is what he sold +n+-+2+ items for
-----------------
He gained 10% overall
+540+%2B+.1%2A540+=+594+
He ended up with $594
+%28+540%2Fn+%2B+6+%29%2A%28+n+-+2+%29+=+594+
+540+%2B+6n+-+1080%2Fn+-+12+=+594+
+6n+=+594+-+528+%2B+1080%2Fn+
+6n%5E2+=+66n+%2B+1080+
+-n%5E2+%2B+11n+%2B+180+=+0+
Use quadratic formula
+n+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-1+
+b+=+11+
+c+=+180+
------------
+n+=+%28-11+%2B-+sqrt%28+11%5E2+-+4%2A%28-1%29%2A180+%29%29+%2F+%282%2A%28-1%29%29+
+n+=+%28-11+%2B-+sqrt%28+121+%2B+720+%29%29+%2F+%28-2%29+%29+
+n+=+%28-11+%2B-+sqrt%28+841+%29%29+%2F+%28-2%29+%29+
+n+=+%28-11+%2B-+29%29+%2F+%28-2%29+%29+
+n+=+%28+-11+-+29+%29+%2F+%28-2%29+
+n+=+20+
(Note that I can't use the (+) square root )
He bought 20 articles
check:
540/20 = 27
He lost 2 and had 18
+18%2A%28+27+%2B+6+%29+=+18%2A33+
+18%2A33+=+594+
This is 10% more that he paid originally
OK