Algebra.Com's Answer #815683 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Marvin decided to rearrange his stamps in his stamp books, Book A, Book B and Book C.
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document.write( "First, he moved 2/9 of the stamps from Book B to Book C.
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document.write( "Then, he moved 3/5 of the remaining stamps from Book B to Book A.
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document.write( "Next, he moved 1/3 of his stamps from Book A to Book C.
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document.write( "In the end, there were 240 fewer stamps in Book B than in Book A.
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document.write( "Book C had 460 more stamps than Book B and there were 600 stamps left in Book C.
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document.write( "How many more stamps were there in Book B than Book A at first?
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document.write( " Looking into the solutions of the two other tutors, I decided to try the backward method, hoping that the solution will be simpler.\r
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document.write( " Let's look what I got ( ! )\r
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document.write( "So, I will accurately divide the entire process by steps.\r\n" );
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document.write( " (1) First, he moved 2/9 of the stamps from Book B to Book C. \r\n" );
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document.write( " (2) Then, he moved 3/5 of the remaining stamps from Book B to Book A. \r\n" );
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document.write( " (3) Next, he moved 1/3 of his stamps from Book A to Book C. \r\n" );
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document.write( " (4) In the end, there were 240 fewer stamps in Book B than in Book A, \r\n" );
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document.write( " and Book C had 460 more stamps than Book B and there were 600 stamps left in Book C. \r\n" );
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document.write( "First of all, based on description of final state (4), we can easily find the number of stamps in each book A, B and C:\r\n" );
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document.write( "  = 600;  = 600 - 460 = 140;  = 140 + 240 = 380.\r\n" );
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document.write( "Next, I will introduce arrays of numbers  ,  ,  ( distribution of stamps immediately before step 1; \r\n" );
document.write( " same as the initial distribution of stamps )\r\n" );
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document.write( "  ,  ,  ( distribution of stamps immediately before step 2) \r\n" );
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document.write( "  ,  ,  ( distribution of stamps immediately before step 3)\r\n" );
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document.write( " , , ( distribution of stamps immediately before step 4)\r\n" );
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document.write( "We just found out the values , , : they are = 380; = 140; = 600.\r\n" );
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document.write( "We will now move from step (4) to step (3). Marvin's action from step (3) to step (4) was \"he moved 1/3 of the stamps from Book A to Book C\". \r\n" );
document.write( " So, we can write\r\n" );
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document.write( " =  , = , = +  .\r\n" );
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document.write( "First of these equations gives =  =  = 570; second gives = 140; third gives = 600 -  = 410.\r\n" );
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document.write( "Thus we can fill the row 3 : = 570; = 140; = 410.\r\n" );
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document.write( "We will now move from step (3) to step (2). Marvin's action from step (2) to step (3) was \"he moved 3/5 of the stamps from Book B to Book A.\"\r\n" );
document.write( " So, we can write\r\n" );
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document.write( " =  , =  , = .\r\n" );
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document.write( "First of these equations gives 570 = ; second gives 140 = ; third gives = 410.\r\n" );
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document.write( "It implies =  = 350; 570 =  = + 210; hence, = 570-210 = 360.\r\n" );
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document.write( "Thus we can fill the row 2 : = 360; = 350; = 410.\r\n" );
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document.write( "We will now move from step (2) to step (1). Marvin's action from step (1) to step (2) was \"he moved 2/9 of the stamps from Book B to Book C.\"\r\n" );
document.write( " So, we can write\r\n" );
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document.write( " = , =  , =  .\r\n" );
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document.write( "First of these equations gives = 360; second gives =  = 450; third gives =  = 310.\r\n" );
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document.write( "Thus we can fill the row 1 : = 360; = 450; = 310.\r\n" );
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document.write( "So the answer to the problem question is - = 450-360 = 90 stamps. ANSWER\r\n" );
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document.write( "Solved.\r
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document.write( "After obtaining this ANSWER, I, naturally, checked it, walking through the steps from (1) to (4).\r
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document.write( "What I got, confirmed correctness of my calculations.\r
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