Question 128020
Verna decided to sell her collection of paperback books.  To Fred, she sold 2 books, and one fifth of what was left.  Later to Joan she sold 6 books, and one fifth of what then remained.  If she sold more books to Fred than Joan, what was the least possible number of books in her original collection?
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Let "x" be the original number of books.
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Sold to Fred:
2+(1/5)(x-2) = (1/5)x+(8/5) = (x+8)/5
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Sold to Joan:
6+(1/5)[(x+8)/5 - 6] = 6+[(x+8)/25]-(6/5) = (x+128)/25
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Your Problem:
She sold more books to Fred that to Joan:
(x+8)/5 > (x+128)/25
5x+40 > x+128
4x > 88
x > 22 books in the original collection.
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Cheers,
Stan H.