Question 1184480
Marvin decided to rearrange his stamps in his stamp books, Book A, Book B and Book C. First, he moved 2/9 of the stamps from Book B to Book C. Then, he moved 3/5 of the remaining stamps from Book B to Book A. Next, he moved 1/3 of his stamps from Book A to Book C. In the end, there were 240 fewer stamps in Book B than in Book A. Book C had 460 more stamps than Book B and there were 600 stamps left in Book C. How many more stamps were there in Book B than Book A at first?
<pre>The other person is PARTLY-WRONG, but that should be expected seeing that the problem's setup and calculations
are difficult enough to easily make mistakes and end up with one or more INCORRECT answers. 

Let number of stamps in Books A, B, and C, be a, b, and c, respectively
After moving {{{2/9}}} from Book B to Book C, Book B then had {{{matrix(1,5, (1 - 2/9), of, b, or, 7b/9)}}} left, and Book C had: {{{matrix(1,5, c + 2/9, of, b, "=", c + 2b/9)}}}  
After moving {{{3/5}}} of remainder from Book B to Book A, Book B then had {{{matrix(1,9, (1 - 3/5), of, 7b/9, or, 2/5, of, 7b/9, "=", 14b/45)}}} left.
Book A then had: {{{matrix(1,5, a + 3/5, of, 7b/9, "=", a + 7b/15)}}}  

After moving {{{1/3}}} from Book A to Book C, Book A then had {{{matrix(1,9, (1 - 1/3), of, (a + 7b/15), or, 2/3, of, (a + 7b/15), "=", 2a/3 + 14b/45)}}} left
Book C then had: {{{matrix(1,5, c + 2b/9 + 1/3, of, (a + 7b/15), "=", c + 2b/9 + a/3 + 7b/45)}}}
As there were 240 fewer stamps in Book B than in Book A, in the end, we get: {{{matrix(3,3, 14b/45, "=", 2a/3 + 14b/45 - 240, 240, "=", 2a/3 + 14b/45 - 14b/45, 240, "=", 2a/3)}}}
                                                                               2a = 3(240) ------- Cross-multiplying
                                                       
                                                Original  number in Book A, or {{{highlight_green(matrix(1,6, a, "=", 3(240)/2, "=", 360, stamps))}}}

As there were 460 more stamps in Book C than in Book B, in the end, we get: {{{matrix(1,3, c + 2b/9 + a/3 + 7b/45 - 460, "=", 14b/45)}}}
  
                                                                              {{{matrix(2,3, 600 - 460, "=",  14b/45, 140, "=", 14b/45)}}} ---- Substituting 600 for {{{c + 2b/9 + a/3 + 7b/45}}}
                                                                              14b = 140(45) ---- Cross-multiplying

                                                Original  number in Book B, or {{{highlight_green(matrix(1,8, b, "=", 140(45)/14, "=", 10(45), "=", 450, stamps))}}}

               Difference between original number in Book A and Book B: {{{highlight_green(matrix(1,4, 450 - 360, "=", 90, stamps))}}}</pre>