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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.

"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

n = [15 ± √(15² + 4·1·250)]/(2·1)
= [15 ± √1225]/2
= [15 ± 35]/2
= -10, 25
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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