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Question
A man purchased a set of identical pictures for $100. Five of the pictures were later damaged. The remainder were sold at a gain of $2 on the original cost of each. As a result $20 was gained on the whole transaction. Calculate original number of pictures.

Answer
"A man purchased a set of identical pictures for $100."
Let n be the number of pictures.
Each picture cost $100/n.

"Five of the pictures were later damaged."
n-5 pictures remained.

"The remainder were sold at a gain of $2 on the original cost of each."
Each was sold for $(100/n + 2).
Total sale = (n-5)(100/n + 2) = 2n - 500/n + 90

"As a result $20 was gained on the whole transaction."
(2n - 500/n + 90) - 100 = 20
n - 15n - 250 = 0

quadratic formula
n = [15 √(15 + 41250)]/(21)
 = [15 √1225]/2
 = [15 35]/2
 = -10, 25
-10 is an extraneous answer
n = 25

Check:
25 pictures were purchased at $4 each, for a total of $100.
20 pictures were sold at $6 each, for a total of $120.
Net gain = $120 - $100 = $20

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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