Question 113462
This a beautifully coined problem.
Solution:
First we find the solution for both Fred and Joan getting equal books.
Then we add one more to Fred logically.
Let the total number of books with Verna = x
Books got by Fred = 2+((x-2)/5) ...first two plus one fifth of (x-2)
Books got by Joan=6+((1/5)x(4/5(x-2)-6)...
equaiting both
1/5(4/5(x-2)-6)+6=((x-2)/5)+2
multiply thro out by 5
(4/5)(x-2)-6+20=x-2
4(x-2)-30+100=5x-10  ...(again x5)
4x-8-30+100=5x-10
100-38=x
72=x
so with 72 books both get equal number of books (14 each) (2 + 70/5)=2+14=16
so for Fred to get one more than Joan you have to add 5 more to Fred ( as denomoiantor is 5 in both cases.
which leads to 2+(F/5)=21
F=95
and total books =95+2=97

Also you can use reduxio ad absurdem mehtod ie from  72 u keep on trying 77, 82 etc till u get a full number for Joan.

Answer 97 books