document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=370991>Question 370991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of two numbers is 105. one-half of one number is equal to one-third of the other number. what are the two numbers?<BR>\n" );
document.write( "thank u !!! (:  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #264327 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=264327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">Let one number be x.  The other number is then (105-x). <br>\r<BR>\n" );
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document.write( "Then we have:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%281%2F2%29=%28105-x%29%2A%281%2F3%29 ALIGN=MIDDLE  ALT=\"x%2A%281%2F2%29=%28105-x%29%2A%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2A%281%2F2%29=6%2A%28105-x%29%2A%281%2F3%29 ALIGN=MIDDLE  ALT=\"6%2Ax%2A%281%2F2%29=6%2A%28105-x%29%2A%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply by 6 on each side to eliminate fractions<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2%2A%28105-x%29 ALIGN=MIDDLE  ALT=\"3x=2%2A%28105-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=210-2x ALIGN=MIDDLE  ALT=\"3x=210-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=210 ALIGN=MIDDLE  ALT=\"5x=210\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=42 ALIGN=MIDDLE  ALT=\"x=42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "So if one number is 42, the other number would be 63.<br>\r<BR>\n" );
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document.write( "However, we are not quite finished, because we can also set it up this way:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%281%2F3%29=%28105-x%29%2A%281%2F2%29 ALIGN=MIDDLE  ALT=\"x%2A%281%2F3%29=%28105-x%29%2A%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > given<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2A%281%2F3%29=6%2A%28105-x%29%2A%281%2F2%29 ALIGN=MIDDLE  ALT=\"6%2Ax%2A%281%2F3%29=6%2A%28105-x%29%2A%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply by 6 on each side to eliminate fractions<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=3%2A%28105-x%29 ALIGN=MIDDLE  ALT=\"2x=3%2A%28105-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=315-3x ALIGN=MIDDLE  ALT=\"2x=315-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=315 ALIGN=MIDDLE  ALT=\"5x=315\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=63 ALIGN=MIDDLE  ALT=\"x=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "And of course, if one number is 63, the other number must be 42.<br>\r<BR>\n" );
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document.write( "This proves that no matter which number you multiply by the fractions of 1/2 and 1/3, you will get the same answer.<br>\r<BR>\n" );
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document.write( "In other words, the two numbers will always be 63 and 42.<br>\r<BR>\n" );
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document.write( "I hope this helps!<br> </SPAN>\n" );
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