document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737364>Question 737364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> mother's age this year is multiple of 5. last year her age was a multiple of 3. she is lessthan 50years and morethan 25years. what is her age?<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 #450327 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=450327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m = mother's age this year.<BR>\n" );
document.write( "n = some unknown whole number.<BR>\n" );
document.write( "i = some unknown whole number, i<>n.\r<BR>\n" );
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document.write( "m=5*n<BR>\n" );
document.write( "m-1=3*i<BR>\n" );
document.write( "m<50 and m>25, or 25<m<50\r<BR>\n" );
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document.write( "The axioms are not seeming to help.  Using the inequality for m and the requirement of m is multiple of 5, the possibilities are m is an element of {30, 35, 40, 45}.\r<BR>\n" );
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document.write( "Last year mother was m-1, which was specified as a multiple of 3.  30-1=29, which will not fit because it's not a multiple of 3.  m-1 is an element of {33, 36, 39, 42, 45, 48 }.  We must adjust this set for m-1+1, so that m-1+1=m which must be an element of {34, 37, 40, 43, 46, 49}.\r<BR>\n" );
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document.write( "We now have two sets for the possible values of m, and m can ONLY be one of those values.  We want the INTERSECTION of the two sets, {30, 35, 40, 45} with {34, 37, 40, 43, 46, 49}.  What element is in BOTH sets?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2840%29 ALIGN=MIDDLE  ALT=\"highlight%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "m=40 this year.  Mother is 40 years of age this year. </SPAN>\n" );
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