document.write( "Question 1193384: Hi
\n" ); document.write( "there were 2222 participants in halls A B and C. During the first interval,3/5 in A went to B .During the second interval, 2/3 of B went over to C. During the last interval,half of C left. In the end there were twice as many participants in C as in B and twice as many participants in B as in A.
\n" ); document.write( "How many were in B at first.
\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #825622 by MathTherapy(10552) $\"\"$ $\"About$

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\n" ); document.write( "Hi
\n" ); document.write( "there were 2222 participants in halls A B and C. During the first interval,3/5 in A went to B .During the second interval, 2/3 of B went over to C. During the last interval,half of C left. In the end there were twice as many participants in C as in B and twice as many participants in B as in A.
\n" ); document.write( "How many were in B at first.
\n" ); document.write( "Thanks
\n" ); document.write( "

The answer from the other person is INCORRECT. It may be correct (not even going to bother to check it) for the WRONG number\r\n" );
document.write( "he used but for a particular given number, that answer is WRONG. Read on for the correct solution and correct answer. \r\n" );
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document.write( "Let original number in A, B, and C, be A, B, and C, respectively\r\n" );
document.write( "We then have: A + B + C = 2,222 ----- eq (i)\r\n" );
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document.write( "After  in A went to B, A had , or  left\r\n" );
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document.write( "After  went to B, B then had:  left\r\n" );
document.write( "After  of the number in B went to C,  B then had  left\r\n" );
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document.write( "After  or  or  went to C, C then had: \r\n" );
document.write( "After ½ of C left, C then had: ½ * , or  left\r\n" );
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document.write( "Since in the end, there were TWICE as many in C as in B, then, \r\n" );
document.write( "            6A + 10B - 15C = 0 ----- Multiplying by LCD, 30 ------ eq (ii)\r\n" );
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document.write( "Since in the end, there were TWICE as many in B as in A, then: \r\n" );
document.write( "                                                                    9A = 5B ----- Cross-multiplying\r\n" );
document.write( "                                                                           \r\n" );
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document.write( "                                                              ------ Substituting  for A in eq (i)\r\n" );
document.write( "                                                          5B + 9B + 9C = 9(2,222) ---- Multiplying by LCD, 9\r\n" );
document.write( "                                                            14B + 9C = 19,998 ------- eq (iv)\r\n" );
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document.write( "                                                      ------ Substituting  for A in eq (ii)\r\n" );
document.write( "                                                      \r\n" );
document.write( "                                                     10B + 30B  -  45C = 0 ------ Multiplying by LCD, 3\r\n" );
document.write( "                                                             10B - 45C = 0 \r\n" );
document.write( "                                                          5(8B  -  9C) = 5(0) \r\n" );
document.write( "                                                           8B  -  9C = 0 ------- eq (v)\r\n" );
document.write( "                                                                   22B = 19,998 ------ Adding eqs (v) & (iv)\r\n" );
document.write( "                                           Original number in B, or

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