document.write( "Question 1013405: how many students are there in a class if 2 students remain after 4 equal rows of seats are filled and one student remains after 3 equal rows of seats are filled? \n" ); document.write( "

Algebra.Com's Answer #629668 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "how many students are there in a class if 2 students remain after 4 equal rows of seats are filled and one student remains after 3 equal rows of seats are filled?
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\n" ); document.write( "\n" ); document.write( "Answer. Possible answers are: 22 students, 34 students, . . . AP with the common difference 12.\r
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document.write( "Solution\r\n" );
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document.write( "Let x be the unknown number of students in the class.\r\n" );
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document.write( "Add 2 to x and consider the number x+2.\r\n" );
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document.write( "According to the condition, it is multiple of 4 and it is multiple of 3.\r\n" );
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document.write( "Hence, it is multiple of 12. Therefore, the number of students in the class is 12n - 2, where n is positive integer.\r\n" );
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document.write( "n=1 gives 10, but it doesn't fit due to other simple reason;\r\n" );
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document.write( "n=2 gives 22 which does suit;\r\n" );
document.write( "n=3 gives 34 which does suit\r\n" );
document.write( ". . . \r\n" );
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