document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=281883>Question 281883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of a number, its reciprocal and 4 times its reciprocal is 6. What is a possible number?\r<BR>\n" );
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document.write( "A) 1	B) 4	C) 6	D) -3	E) -1\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204732 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><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=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=204732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The most obvious answer I try when seeing questions like this is 1 since 1 and its reciprocal 1/1 is also 1 and adding the reciprocal any number of times will always give another whole number. There are others but they are not so obvious.\r<BR>\n" );
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document.write( "So let us take you to the solution.\r<BR>\n" );
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document.write( "Suppose the number is x\r<BR>\n" );
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document.write( "Then x + 1/x + 4/x = 6\r<BR>\n" );
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document.write( "x + 5/x = 6\r<BR>\n" );
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document.write( "x^2 + 5 = 6x\r<BR>\n" );
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document.write( "Giving\r<BR>\n" );
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document.write( "x^2 - 6x + 5 = 0\r<BR>\n" );
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document.write( "(x - 5)(x - 1) = 0\r<BR>\n" );
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document.write( "x - 5 = 0 and x - 1 = 0 as solutions\r<BR>\n" );
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document.write( "So we have x = 1 and x = 5\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "1 + 1/1 + 4/1 = 6\r<BR>\n" );
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document.write( "5 + 1/5 + 4/5 = 6\r<BR>\n" );
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document.write( "The answer 5 wasn’t given in the options for your answer. </SPAN>\n" );
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