document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878712>Question 878712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number is such that it is as much greater than 84 as it is less than 108. find it<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 #530226 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=530226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> MENTAL MATH:<BR>\n" );
document.write( "I would average the two numbers in my head, and come up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2896%29 ALIGN=MIDDLE  ALT=\"highlight%2896%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In my head I really average their differences to 100.<BR>\n" );
document.write( "I see 84 as 84 - 100 = -16, and I see 108 as 8.<BR>\n" );
document.write( "I add -16+8=-8, and divide by 2 to find the average as -4.<BR>\n" );
document.write( "That means that the number is -4 + 100 = 96.<BR>\n" );
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document.write( "SYSTEM OF EQUATIONS:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the number<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= how much greater than 84 the number is<BR>\n" );
document.write( "Since the number is that much greater than 84 the number is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=84%2By ALIGN=MIDDLE  ALT=\"x=84%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since the number is that much less than 108 the number is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=108-y ALIGN=MIDDLE  ALT=\"x=108-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So we write the system of equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=84%2By%2Cx=108-y%29 ALIGN=MIDDLE  ALT=\"system%28x=84%2By%2Cx=108-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we solve it by institution, substituting the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108-y ALIGN=MIDDLE  ALT=\"108-y\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%7D%7D+in+%7B%7B%7Bx=84%2By ALIGN=MIDDLE  ALT=\"x%7D%7D+in+%7B%7B%7Bx=84%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > , to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108-y=84%2By ALIGN=MIDDLE  ALT=\"108-y=84%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We 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;\" > , and then we plug the value found 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;\" > into either of the original equations yo 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;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108-y=84%2By ALIGN=MIDDLE  ALT=\"108-y=84%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108=84%2By%2By ALIGN=MIDDLE  ALT=\"108=84%2By%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108=84%2B2y ALIGN=MIDDLE  ALT=\"108=84%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108-84=2y ALIGN=MIDDLE  ALT=\"108-84=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=2y ALIGN=MIDDLE  ALT=\"24=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F2=y ALIGN=MIDDLE  ALT=\"24%2F2=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=12%29 ALIGN=MIDDLE  ALT=\"highlight%28y=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=84%2By%2Cy=12%29 ALIGN=MIDDLE  ALT=\"system%28x=84%2By%2Cy=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=84%2B12 ALIGN=MIDDLE  ALT=\"x=84%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=96%29 ALIGN=MIDDLE  ALT=\"highlight%28x=96%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "There are many other ways to solve it. </SPAN>\n" );
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