document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921289>Question 921289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Positive integers x and y have a product of 56 and x < y. Seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4. What is the value of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805659 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=805659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> xy = 56<BR>\n" );
document.write( "7(1/x) + 14(1/y) = 4\r<BR>\n" );
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document.write( "Simplify the second equation.<BR>\n" );
document.write( "7/x + 14/y = 4<BR>\n" );
document.write( "(7y + 14x)/(xy) = 4<BR>\n" );
document.write( "7y + 14x = 4 * 56 = 224 ----> 2x + y = 32 ---> y = 32 - 2x\r<BR>\n" );
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document.write( "Substitute this into the first equation.\r<BR>\n" );
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document.write( "xy = 56<BR>\n" );
document.write( "x(32 - 2x) = 56<BR>\n" );
document.write( "-2x^2 + 32x - 56 = 0<BR>\n" );
document.write( "x^2 - 16x + 28 = 0<BR>\n" );
document.write( "(x - 2)(x - 14) = 0\r<BR>\n" );
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document.write( "x is the smaller integer, so x = 2 and y = 28. </SPAN>\n" );
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