document.write( "Question 1180494: in yoga class, all of the students are lined up according to height. Andy notices that the number of students who are taller than he is one-fourth the number of students who are shorter than he. Violetta notices that there are 3 times as many students who are taller than she than students who are shorter than she. How many students are the class is there are fewer than 40 students? \n" ); document.write( "

Algebra.Com's Answer #810186 by ikleyn(52810) $\"\"$ $\"About$

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\n" ); document.write( "in yoga class, all of the students are lined up according to height.
\n" ); document.write( "Andy notices that the number of students who are taller than he is one-fourth the number of students who are shorter than he.
\n" ); document.write( "Violetta notices that there are 3 times as many students who are taller than she than students who are shorter than she.
\n" ); document.write( "How many students are the class is there are fewer than 40 students?
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document.write( "First, consider Andy.\r\n" );
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document.write( "    Let x be the number of students who are taller than he.\r\n" );
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document.write( "    Then the number of the rest students, excluding him, is 4x, according to the condition.\r\n" );
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document.write( "    So, the total number of students in the class is  (x + 4x + 1),  or  5x+1.\r\n" );
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document.write( "Next, consider Violette.\r\n" );
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document.write( "    Let y be the number of students who are shorter than she.\r\n" );
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document.write( "    Then the number of the rest students, excluding her, is 3y, according to the condition.\r\n" );
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document.write( "    So, the total number of students in the class is  (y + 3y + 1),  or  4y+1.\r\n" );
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document.write( "We see, that  the number of students in the class MINUS one  is a multiple of 4 (four) and of 5 (five), at the same time.\r\n" );
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document.write( "So, the number of students in the class is EITHER  20+1 = 21  OR  40+1 = 41,  if consider couple of minimal values.\r\n" );
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document.write( "But 41 is excluded by the condition, leaving a UNIQUE ANSWER:\r\n" );
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document.write( "    |  The number of students in the class is 21.     |\r\n" );
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