Question 113462
I know the answer, which is 97, because I found it in the back of the book, but I can't figure out how to solve the problem and I need to show work. Please help me with the steps. The question is:

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 to Joan what was the least possible number of books in her original collection?
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Let b be the amt. she started with.
Sold to Fred: 2+(b-2)/5
Sold to Joan: 6+(b-6-2+((b-2)/5))/5
2+((b-2)/5))>6+(b-6-2-((b-2)/5))/5
10+b-2>30+b-6-2-((b-2)/5)) multiply both sides by 5
50+5b-10>150+5b-30-10-b+2 multiply both sides by 5 again
5b+40>112+4b
b>72
At b=72 Fred and Joan have an equal number of books (16 each)
At b=73 Fred will have more books but he can't have a round number because of the division by 5. Both Joan and Fred can't both have a round number except for every 25 because of the second division by 5.
72+25=97
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That was super tough!!!
Ed