document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007123>Question 1007123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help!<BR>\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?<BR>\n" );
document.write( "A) x<y<z<BR>\n" );
document.write( "B) y<x<z<BR>\n" );
document.write( "C) z<x<y<BR>\n" );
document.write( "D) y<x z </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623115 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> xy = 24 yields y = 24/x<BR>\n" );
document.write( "yz = 56 yields y = 56/z\r<BR>\n" );
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document.write( "y equal to both yields 24/x = 56/z<BR>\n" );
document.write( "that leads to 24z = 56x<BR>\n" );
document.write( "that leads to z = 56x/24\r<BR>\n" );
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document.write( "that means that z has to be greater than x and the ratio of z to x has to be 56/24.\r<BR>\n" );
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document.write( "since 56/24 is not an integer, then x has to be a multiple of whatever makes 56/24 * x an integer.\r<BR>\n" );
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document.write( "56/24 reduces to 7/3.\r<BR>\n" );
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document.write( "x can be equal to 3,6,9,12,15,18,.....\r<BR>\n" );
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document.write( "in other words x can be a multiple of 3.\r<BR>\n" );
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document.write( "but not all multiples of 3 will work.\r<BR>\n" );
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document.write( "that's because xy has to be equal to 24.\r<BR>\n" );
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document.write( "when x = 3, y is equal to 8.<BR>\n" );
document.write( "when x = 6, y is equal to 4.<BR>\n" );
document.write( "when x = 9, y is not an integer.<BR>\n" );
document.write( "when x = 12, y is equal to 2.<BR>\n" );
document.write( "when x = 15, y is not an integer.<BR>\n" );
document.write( "when x = 18, y is not an integer.<BR>\n" );
document.write( "hen x = 21, y is not an integer.<BR>\n" );
document.write( "when x = 24, y is equal to 1 which is not greater than 1.\r<BR>\n" );
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document.write( "the only possible values of x are 3 or 6 or 12.\r<BR>\n" );
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document.write( "when x is 3, y is 8, and z is 7 because xy = 24 and yz = 56.<BR>\n" );
document.write( "you get x < z < y<BR>\n" );
document.write( "that is not one of the selections.\r<BR>\n" );
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document.write( "when x is 6, y is 4 and z is 14 because 6*4 = 24 and 4*14 = 56.<BR>\n" );
document.write( "you get y < x < z<BR>\n" );
document.write( "that is selection B.\r<BR>\n" );
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document.write( "when x is 12, y is 2 and z is 28 because 12*2 = 24 and 2*28 = 56.<BR>\n" );
document.write( "you get y < x < z<BR>\n" );
document.write( "this is selection B.\r<BR>\n" );
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document.write( "i would go with selection B.<BR>\n" );
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