SOLUTION: The cost to develop a DVD is $300,000. DVDs can be made for $0.27 each. Two hundred DVDs are given away as samples. How many DVDs must be produced for the average cost to be under

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Question 697046: The cost to develop a DVD is $300,000. DVDs can be made for $0.27 each. Two hundred DVDs are given away as samples. How many DVDs must be produced for the average cost to be under $12?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +C+ = the cost to produce +n+ DVD's
which do not include the +200+ samples
The $300,000 is a fixed cost, and the +200+
that are given away is a fixed cost. This fixed cost
is the +200%2A.27+ production cost of
the samples
+C+=+.27n+%2B+300000+%2B+200%2A.27++
+C+=+.27n+%2B+300000+%2B+54+
+C+=+.27n+%2B+300054+
The average cost is required to be
+C+%2F+%28+n+%2B+200+%29+%3C+12+
Substituting,
+%28+.27n+%2B+300054+%29+%2F+%28+n+%2B+200+%29+%3C+12+
+.27n+%2B+300054++%3C+12%2A%28+n+%2B+200+%29+
+.27n+%2B+300054+%3C+12n+%2B+2400+
+11.73n+%3E+300054+-+2400+
+11.73n+%3E+297654+
+n+%3E+25375.5+
+n+%2B+200+%3E+25575.5+
25,577 DVDs must be produced for the
average cost to be under $12
-----------------
check answer:
+C+=+.27n+%2B+300054+
+C+=+.27%2A25377+%2B+300054+
+C+=+6851.79+%2B+300054+
+C+=+306905.79+
+C+%2F+%28+n+%2B+200+%29+%3C+12+
+306905.79+%2F+%28+n+%2B+200+%29+%3C+12+
+306905.79+%2F+%28+25377+%2B+200+%29+%3C+12+
+306905.79+%2F+25577+%3C+12+
+11.999+%3C+12+
OK
Hope I got it!