SOLUTION: Finding number of books. 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

Question 128020This question is from textbook Algebra structure and method book 1
: Finding number of books. 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? This question is from textbook Algebra structure and method book 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.

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