document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123470>Question 1123470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if three positive integers are added two at a time, the sums are 998, 1050, and 1234. the difference between the largest and the smallest number is:<BR>\n" );
document.write( "A) 224<BR>\n" );
document.write( "B) 236<BR>\n" );
document.write( "C) 248<BR>\n" );
document.write( "D) 250<BR>\n" );
document.write( "E) 262 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739811 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( " let’s three positive integers be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if added two at a time, we have sums as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By ALIGN=MIDDLE  ALT=\"x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bz ALIGN=MIDDLE  ALT=\"x%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz ALIGN=MIDDLE  ALT=\"y%2Bz\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " if the sums are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=998 ALIGN=MIDDLE  ALT=\"998\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1050 ALIGN=MIDDLE  ALT=\"1050\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1234 ALIGN=MIDDLE  ALT=\"1234\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=998 ALIGN=MIDDLE  ALT=\"x%2By=998\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bz=1050 ALIGN=MIDDLE  ALT=\"x%2Bz=1050\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz=1234 ALIGN=MIDDLE  ALT=\"y%2Bz=1234\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3<BR>\n" );
document.write( "--------------------------------------------solve this system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=998 ALIGN=MIDDLE  ALT=\"x%2By=998\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x=998-y ALIGN=MIDDLE  ALT=\"x=998-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bz=1050 ALIGN=MIDDLE  ALT=\"x%2Bz=1050\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.2....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x=1050-z ALIGN=MIDDLE  ALT=\"x=1050-z\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.b\r<BR>\n" );
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document.write( "from eq.a and eq.b we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=998-y=1050-z ALIGN=MIDDLE  ALT=\"998-y=1050-z\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=998-1050%2Bz=y ALIGN=MIDDLE  ALT=\"998-1050%2Bz=y\"   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=y=z+-52 ALIGN=MIDDLE  ALT=\"y=z+-52\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................eq.c\r<BR>\n" );
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document.write( "substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Bz=1234 ALIGN=MIDDLE  ALT=\"y%2Bz=1234\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-52%2Bz=1234 ALIGN=MIDDLE  ALT=\"z-52%2Bz=1234\"   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=2z=1234%2B52 ALIGN=MIDDLE  ALT=\"2z=1234%2B52\"   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=2z=1286 ALIGN=MIDDLE  ALT=\"2z=1286\"   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=z=1286%2F2 ALIGN=MIDDLE  ALT=\"z=1286%2F2\"   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=highlight%28z=643%29 ALIGN=MIDDLE  ALT=\"highlight%28z=643%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=z+-52 ALIGN=MIDDLE  ALT=\"y=z+-52\"   DISABLED_style= \"max-width:90%; height:auto;\" >.................eq.c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=643+-52 ALIGN=MIDDLE  ALT=\"y=643+-52\"   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=highlight%28y=591%29 ALIGN=MIDDLE  ALT=\"highlight%28y=591%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x=998-y ALIGN=MIDDLE  ALT=\"x=998-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=998-591 ALIGN=MIDDLE  ALT=\"x=998-591\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=407%29 ALIGN=MIDDLE  ALT=\"highlight%28x=407%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so your numbers are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28643%29 ALIGN=MIDDLE  ALT=\"highlight%28643%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the largest<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28591%29 ALIGN=MIDDLE  ALT=\"highlight%28591%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28407%29 ALIGN=MIDDLE  ALT=\"highlight%28407%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the smallest \r<BR>\n" );
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document.write( "and, the difference between the largest and the smallest number is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28643-407=236%29 ALIGN=MIDDLE  ALT=\"highlight%28643-407=236%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your answer is: B) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=236 ALIGN=MIDDLE  ALT=\"236\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );