document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113476>Question 113476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary is ten years younger than twice Susan's age. Five years from now, Mary will be eight years older than Susan's age at the time. How old are Mary and Susan?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82542 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say Mary is m years old, and Susan is s years old.  So twice Susan's age is 2s.  Ten years younger than that is 2s - 10.  Since that is Mary's age now, we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+2s+-+10 ALIGN=MIDDLE  ALT=\"m+=+2s+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Five years from now, Mary will be m + 5 years old, and Susan will be s + 5 years old.  And the problem tells us that Mary will be eight years older than Susan then.  So we can also write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+%2B+5=s%2B5%2B8 ALIGN=MIDDLE  ALT=\"m+%2B+5=s%2B5%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2B5=s%2B13 ALIGN=MIDDLE  ALT=\"m%2B5=s%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2s-10 ALIGN=MIDDLE  ALT=\"m=2s-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can substitute this expression in the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282s-10%29%2B5=s%2B13 ALIGN=MIDDLE  ALT=\"%282s-10%29%2B5=s%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now solve for s:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s-5=s%2B13 ALIGN=MIDDLE  ALT=\"2s-5=s%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Collect terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2s-s=13%2B5 ALIGN=MIDDLE  ALT=\"2s-s=13%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add -s and +5 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=18 ALIGN=MIDDLE  ALT=\"s=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So Susan is 18.  Let's put this value back into the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2%2818%29-10 ALIGN=MIDDLE  ALT=\"m=2%2818%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=26 ALIGN=MIDDLE  ALT=\"m=26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And Mary is 26.\r<BR>\n" );
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document.write( "Last step -- Very Important.  Check your answer.\r<BR>\n" );
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document.write( "26 = 2 * 18 - 10, 26 = 26 Check and<BR>\n" );
document.write( "26 + 5 = 18 + 13, 31 = 31 And both answers check.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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