document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344416>Question 344416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 1/6 is added to 4 times the reciprocal of a certain number, the result is 21/10. Find the number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246344 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=246344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is the reciprocal of y if x*y = 1.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "The reciprocal of 3 is equal to 1/3 because 3 * 1/3 = 1\r<BR>\n" );
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document.write( "Let x equal the reciprocal of y.\r<BR>\n" );
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document.write( "You get 1/6 + 4*x = 21/10.\r<BR>\n" );
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document.write( "Multiply both sides of this equation by 60 to get:\r<BR>\n" );
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document.write( "10 + 240 * x = 126\r<BR>\n" );
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document.write( "Subtract 10 from both sides of this equation to get:\r<BR>\n" );
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document.write( "240*x = 116\r<BR>\n" );
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document.write( "Divide both sides of this equation by 240 to get:\r<BR>\n" );
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document.write( "x = 116 / 240\r<BR>\n" );
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document.write( "Since x is the reciprocal of y, this means that y is equal to 240 / 116\r<BR>\n" );
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document.write( "The number you are looking for should be 240 / 116.\r<BR>\n" );
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document.write( "To find out if that is true, substitute 240 / 116 for the number in your original problem statement.\r<BR>\n" );
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document.write( "The original problem statement is:\r<BR>\n" );
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document.write( "If 1/6 is added to 4 times the reciprocal of a certain number, the result is 21/10. Find the number.\r<BR>\n" );
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document.write( "If the number is 240 / 116, then the reciprocal of the number has to be 116 / 240 because 240 / 116 * 116 / 240 = 1.\r<BR>\n" );
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document.write( "So, the reciprocal we are looking for is 116 / 240.\r<BR>\n" );
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document.write( "4 * 116 / 240 = 464 / 240.\r<BR>\n" );
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document.write( "Add 1/6 to that and you get:\r<BR>\n" );
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document.write( "464 / 240 + 1/6 = 464 / 240 + 40 / 240 = 504 / 240\r<BR>\n" );
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document.write( "If this is correct, then 504 / 240 should be equal to 21 / 10\r<BR>\n" );
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document.write( "If you divide numerator and denominator of 504 / 240 by 24, then you get 21 / 10 which is the same as 21 / 10, so the answer is good.\r<BR>\n" );
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document.write( "The number you are looking for is 240 / 116.\r<BR>\n" );
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document.write( "The reciprocal of that number is 116 / 240.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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