document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132598>Question 132598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a certain positive number is added to 4 times the reciprocal of 10 less than the number, the result is 5.  What is one of the numbers?<BR>\n" );
document.write( "a. -6<BR>\n" );
document.write( "b. -10<BR>\n" );
document.write( "c. -9<BR>\n" );
document.write( "d. 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96906 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=96906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=the certain positive number\r<BR>\n" );
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document.write( "10 less than this number is x-10<BR>\n" );
document.write( "The reciprocal of 10 less than the number is 1/(x-10)<BR>\n" );
document.write( "4 times the reciprocal is 4/(x-10)\r<BR>\n" );
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document.write( "Now we are told the following:\r<BR>\n" );
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document.write( "x + 4/(x-10)=5  multiply each term by (x-10)<BR>\n" );
document.write( "x(x-10)+4=5(x-10)  get rid of parens\r<BR>\n" );
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document.write( "x^2-10x+4=5x-50  subtract 5x from and add 50 to both sides\r<BR>\n" );
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document.write( "x^2-10x-5x+4+50=5x-5x-50+50  collect like terms\r<BR>\n" );
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document.write( "x^2-15x+54=0   quadratic in standard form and it can be factored:\r<BR>\n" );
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document.write( "(x-6)(x-9)=0\r<BR>\n" );
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document.write( "x-6=0<BR>\n" );
document.write( "x=6-----------------------possible solution<BR>\n" );
document.write( "x-9=0<BR>\n" );
document.write( "x=9---------------------------another possible solution\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "for x=6<BR>\n" );
document.write( "6+4/(6-10)=5<BR>\n" );
document.write( "6-1=5<BR>\n" );
document.write( "5=5-----------------------------x=6 is a solution<BR>\n" );
document.write( "for x=9<BR>\n" );
document.write( "6+4/(9-10)=5<BR>\n" );
document.write( "6-4=5<BR>\n" );
document.write( "2=5------------------------------x=9 is not a solution\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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