document.write( "Question 1007123: Please help!
\n" ); document.write( "If x,y,z are integers greater than 1 and if xy =24 and yz=56,which of the following must be true? and how?
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Algebra.Com's Answer #623109 by Edwin McCravy(20060) $\"\"$ $\"About$

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Please help!
\n" ); document.write( "If x,y,z are integers greater than 1 and if xy =24 and yz=56,
\n" ); document.write( "which of the following must be true? and how?
\n" ); document.write( "A) x < y < z
\n" ); document.write( "B) y < x < z
\n" ); document.write( "C) z < x < y
\n" ); document.write( "D) y < x z
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document.write( "We are given: xy =24 and yz=56.  Therefore,\r\n" );
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document.write( "y= 24/x  and y = 56/z, so\r\n" );
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document.write( "24/x = 56/z\r\n" );
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document.write( "24z = 56x\r\n" );
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document.write( " 3z = 7x\r\n" );
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document.write( "z/x = 7/3 = 14/6 = 21/9 = 28/12\r\n" );
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document.write( "So the potential solutions are\r\n" );
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document.write( "(z,x) = (7,3), (14,6), (21,9), (28/12)\r\n" );
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document.write( "y = 56/z so we must rule out (21,9) because 21 is not a \r\n" );
document.write( "factor of 56.\r\n" );
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document.write( "So the only possibilities for (z,x) are these three\r\n" );
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document.write( "(z,x) = (7,3), (14,6), (28/12) \r\n" );
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document.write( "Which means, using y=56/z, the only possibilities for (x,y,z) are\r\n" );
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document.write( "(x,y,z) = (3,8,7), (6,4,14), and (12,2,28)\r\n" );
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document.write( "Therefore z is always greater than x,  \r\n" );
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document.write( "But something is wrong with the choices listed above:\r\n" );
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document.write( "In the case (x,y,z) = (3,8,7)\r\n" );
document.write( "we have 3 < 7 < 8, or x < z < y which is none of those.\r\n" );
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document.write( "In the case (x,y,z) = (6,4,14)\r\n" );
document.write( "we have 4 < 6 < 14, or y < x < z which is B.\r\n" );
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document.write( "In the case (x,y,z) = (12,2,28)\r\n" );
document.write( "we have 2 < 12 < 28, or y < x < z which is B.\r\n" );
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document.write( "So, as this clearly proves, none of those choices are always true.\r\n" );
document.write( "B is true for only 2 of the 3 solutions, and none of them is\r\n" );
document.write( "true for (x,y,z)=(3,8,7) \r\n" );
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document.write( "Edwin

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