document.write( "Question 250090: Jenny says, \"I'm the sixth child in my family, and I have at least as many brothers as sisters.\" Her brother Jim adds, \"I have at least twice as many sisters as brothers.\" How many boys and girls are in their family? \n" ); document.write( "

Algebra.Com's Answer #182074 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "You can probably do this problem by trial and error,\r\n" );
document.write( "but more complicated problems similar to this which have\r\n" );
document.write( "more given restrictions cannot be.  So to learn the methods\r\n" );
document.write( "we must do this algebraically and graphically by the use \r\n" );
document.write( "of linear inequalities.\r\n" );
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document.write( "Here's how to solve it algebraically:\r\n" );
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document.write( "Let x = the number of girls\r\n" );
document.write( "Let y = the number of boys\r\n" );
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document.write( "Jenny has y brothers and x-1 sisters (Jenny is not her own sister,\r\n" );
document.write( "so we must eliminate her from the girls who can be Jenny's sisters\r\n" );
document.write( "by subtracting 1)\r\n" );
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document.write( "Jim has x sisters and y-1 brother (Jim is not his own brother, so we\r\n" );
document.write( "must eliminate him from the boys who can be Jim's brothers, also by\r\n" );
document.write( "subtracting 1)\r\n" );
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document.write( "Since Jenny is the 6th child, the total of the girls and boys must\r\n" );
document.write( "be 6 or more.  Therefore, \r\n" );
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document.write( "By Jenny's statement, \r\n" );
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document.write( "By Jim's statement, \r\n" );
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document.write( "So we have the system of inequalities:\r\n" );
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document.write( "We graph the boundary lines, which are the inequalities\r\n" );
document.write( "with equality signs instead of inequality signs:\r\n" );
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document.write( "The correct solution point must be \r\n" );
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document.write( "1.  on or above the red line,\r\n" );
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document.write( "2.  on or above the green line, and \r\n" );
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document.write( "3.  on or below the blue line.\r\n" );
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document.write( "Therefore the solution point is either inside or on the \r\n" );
document.write( "little triangle bounded by the three lines.\r\n" );
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document.write( "Also, the solution point must \r\n" );
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document.write( "4.  have whole number coordinates,\r\n" );
document.write( "as we cannot have fractions of people!\r\n" );
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document.write( "Therefore the only point in or on the triangle\r\n" );
document.write( "which has all four properties above is the point (4,3), \r\n" );
document.write( "which is marked.  Thus x=4, y=3 and there are 4 girls \r\n" );
document.write( "and 3 boys.\r\n" );
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document.write( "Checking: \r\n" );
document.write( "Jenny has 3 brothers and 3 sisters, so she has at least \r\n" );
document.write( "as many brothers as sisters, in fact, the same number.\r\n" );
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document.write( "Jim has 4 sisters and 2 brothers, so he has at least \r\n" );
document.write( "twice as many sisters as he has brothers, in fact, \r\n" );
document.write( "exactly twice as many.\r\n" );
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document.write( "Edwin

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