document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107477>Question 107477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One number is 3 times another. If the sum of their reciprocals<BR>\n" );
document.write( "Is 1/6, find the two numbers.<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 #78282 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=first number, y=second number\r<BR>\n" );
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document.write( "Since one number (say the first number) is 3 times the other, then\r<BR>\n" );
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document.write( "Now the statement \"..the sum of their reciprocals<BR>\n" );
document.write( "Is 1/6\" translates to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%2B1%2Fy=1%2F6 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2Fy=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283y%29%2B1%2Fy=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F%283y%29%2B1%2Fy=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3y ALIGN=MIDDLE  ALT=\"x=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283y%29%2B%281%2Fy%29%283%2F3%29=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F%283y%29%2B%281%2Fy%29%283%2F3%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get to the common denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y ALIGN=MIDDLE  ALT=\"3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283y%29%2B%283%29%2F%283y%29=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F%283y%29%2B%283%29%2F%283y%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B3%29%2F%283y%29=1%2F6 ALIGN=MIDDLE  ALT=\"%281%2B3%29%2F%283y%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%283y%29=1%2F6 ALIGN=MIDDLE  ALT=\"4%2F%283y%29=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the numerators\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=%283y%29%2F6 ALIGN=MIDDLE  ALT=\"4=%283y%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 3y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=3y ALIGN=MIDDLE  ALT=\"24=3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=y ALIGN=MIDDLE  ALT=\"8=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to solve for y\r<BR>\n" );
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document.write( "So one number is 8\r<BR>\n" );
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document.write( "Now multiply 8 by 3 to find the first number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2A8=24 ALIGN=MIDDLE  ALT=\"x=3%2A8=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So another number is 24\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24 ALIGN=MIDDLE  ALT=\"y=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Remember their reciprocals should add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8%2B1%2F24 ALIGN=MIDDLE  ALT=\"1%2F8%2B1%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Turn 8 into 1/8 and 24 into 1/24\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F24%2B1%2F24 ALIGN=MIDDLE  ALT=\"3%2F24%2B1%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 1/8 by 3/3\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F24 ALIGN=MIDDLE  ALT=\"4%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the fractions \r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So our answer is verified\r<BR>\n" );
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document.write( "note: the previous answer is incorrect. When you check by adding the reciprocal of 3/2 and 9/2 you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3%2B2%2F9=6%2F9%2B2%2F9=8%2F9 ALIGN=MIDDLE  ALT=\"2%2F3%2B2%2F9=6%2F9%2B2%2F9=8%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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