document.write( "Question 1099228: Students of a class are made to stand in rows.\r
\n" ); document.write( "\n" ); document.write( "if one student is Extra in each row, there would be 2 rows less in the arrangement.
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Algebra.Com's Answer #713664 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The original arrangement of the class is S students in each of R rows.\r\n" );
document.write( "So SR = the number of students in the class.\r\n" );
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document.write( "The first new arrangement of the class is S+1 students in each of R-2 rows.\r\n" );
document.write( "So (S+1)(R-2) also equals the number of students in the class.\r\n" );
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document.write( "The second new arrangement of the class is S-1 students in each of R+3 rows.\r\n" );
document.write( "So (S-1)(R+3) also equals the students in the class.\r\n" );
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document.write( "Since the number of students is the same under each of the three\r\n" );
document.write( "arrangements,\r\n" );
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document.write( "SR = (S+1)(R-2) = (S-1)(R+3)\r\n" );
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document.write( "SR =  SR-2S+R-2 =  SR+3S-R-3\r\n" );
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document.write( "Subtract SR from all three sides:\r\n" );
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document.write( " 0 =    -2S+R-2 =     3S-R-3 \r\n" );
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document.write( "So each of those are equal to 0\r\n" );
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document.write( "-2S+R-2 = 0    \r\n" );
document.write( " 3S-R-3 = 0\r\n" );
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document.write( "Adding the two equations term by term:\r\n" );
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document.write( "  S -5 = 0\r\n" );
document.write( "     S = 5\r\n" );
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document.write( "Substituting S = 5 in -2S+R-2 = 0 \r\n" );
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document.write( "-2(5)+R-2 = 0\r\n" );
document.write( "  -10+R-2 = 0\r\n" );
document.write( "    -12+R = 0\r\n" );
document.write( "        R = 12\r\n" );
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document.write( "So the number of students is SR = (5)(12) = 60\r\n" );
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document.write( "Checking.\r\n" );
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document.write( "In the original arrangement there were 5 students in each of 12 rows.\r\n" );
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document.write( "In the first new arrangement there were 6 students in each of 10 rows.\r\n" );
document.write( "That's 1 student more and 2 rows less than in the original arrangement. \r\n" );
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document.write( "In the second new arrangement there were 4 students in each of 15 rows.\r\n" );
document.write( "That's 1 student less and 3 rows more than in the original arrangement. \r\n" );
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document.write( "Edwin
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