document.write( "Question 1161746: In an indoor games tournament at Sekolah Menengah Tanjung Malim, medals are
\n" ); document.write( "awarded in three games. 36 medals in chess game, 12 medals in scrabble and 18
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\n" ); document.write( "If these medals went to a total of 45 students and only 4 students got medals in all
\n" ); document.write( "three games, how many students received medals in exactly two of these games?
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Algebra.Com's Answer #785393 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "In an indoor games tournament at Sekolah Menengah Tanjung Malim, medals are awarded in three games:
\n" ); document.write( "36 medals in chess game, 12 medals in scrabble and 18 medals in sahibba.
\n" ); document.write( "If these medals went to a total of 45 students and only 4 students got medals in all three games,
\n" ); document.write( "how many students received medals in exactly two of these games?
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document.write( "Let C (chess), B (scrabble) and H (sahiba) be the abbreviations for these games.\r\n" );
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document.write( "Let p is the number of students having medals in the game C only.\r\n" );
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document.write( "Let q is the number of students having medals in the game B only.\r\n" );
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document.write( "Let r is the number of students having medals in the game H only.\r\n" );
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document.write( "Let x is the number of students having medals in exactly two games C and B.\r\n" );
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document.write( "Let y is the number of students having medals in exactly two games C and H.\r\n" );
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document.write( "Let z is the number of students having medals in exactly two games B and H.\r\n" );
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document.write( "    The problem asks about the amount x+y+z.\r\n" );
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document.write( "From the condition, we have these equations\r\n" );
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document.write( "    p + x + y + 4 = 36     (1)\r\n" );
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document.write( "    q + x + z + 4 = 18     (2)\r\n" );
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document.write( "    r + y + z + 4 = 12     (3)\r\n" );
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document.write( "Add equations (1), (2) and (3).   You will get\r\n" );
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document.write( "    (p + q + r) + 2*(x + y + z) + 3*4 = 36 + 18 + 12,   or\r\n" );
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document.write( "    (p + q + r) + 2*(x + y + z) +   4 = 66 - 8,         or\r\n" );
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document.write( "    (p + q + r) + 2*(x + y + z) +   4 = 58.    (4)\r\n" );
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document.write( "From the other side, from the condition, we have another equation \r\n" );
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document.write( "    (p + q + r) +   (x + y + z) +   4  = 45    (5)\r\n" );
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document.write( "for the total number of students.\r\n" );
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document.write( "Now subtract equation (5) from equation (4).    You will get\r\n" );
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document.write( "    x + y + z = 58 - 45 = 13.\r\n" );
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document.write( "This value  x + y + z = 13  is the desired ANSWER.\r\n" );
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document.write( "ANSWER.  The number of students received medals in exactly two of these games is 13.\r\n" );
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