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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.

"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

n² - 15n - 250 = 0

quadratic formula

n = [15 ± √(15² + 4·1·250)]/(2·1)

= [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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