document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29192>Question 29192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I'm older but new at word problems.  We are using labels x Per = Total to solve<BR>\n" );
document.write( "this word problem.\r<BR>\n" );
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document.write( "Two clothing businesses are merged into one.  At Men's Mercantile, 40% of the employees are women.  At Women's Wear 80% are women.  After the merger, 70% of the 2000 employees are women.  How many employees were employed by each business before the merger? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16022 by </B><A HREF=/tutors/aboutme.mpl?userid=bmauger><B>bmauger(101)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bmauger><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=16022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sometimes it helps to think backwards...<br><BR>\n" );
document.write( "The question ultimately asks us how many employees were employed by each business. Since these are the values we're ultimately trying to solve for, we'll call the # working at Men's Mercantile \"m\" and the number at Women's Wear \"w\".<BR>\n" );
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document.write( "After the merger there are 2000 employees. Thus when you add the number working at Men's Mercantile \"m\" with \"w\" you get 2000. Or:<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bw=2000 ALIGN=MIDDLE  ALT=\"m%2Bw=2000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problem also tells us that 70% of those 2000 are women, thus: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.70%2A2000=1400 ALIGN=MIDDLE  ALT=\".70%2A2000=1400\"   DISABLED_style= \"max-width:90%; height:auto;\" > 1400 are women.<BR>\n" );
document.write( "If 40% working at Men's Mercantile are women, then we can write the number of women at MM as 40% of m or .4 times m. We can also see that the number of women working at Women's Wear is .8w. When we add the numbers up we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.4m%2B.8w=1400 ALIGN=MIDDLE  ALT=\".4m%2B.8w=1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We now have two equations and can solve for both variables. Using substitution we can rewrite Equation 1 as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2000-w ALIGN=MIDDLE  ALT=\"m=2000-w\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we can substitute for m in equation 2 with 2000-w and write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.4%282000-w%29%2B.8w=1400 ALIGN=MIDDLE  ALT=\".4%282000-w%29%2B.8w=1400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800-.4w%2B.8w=1400 ALIGN=MIDDLE  ALT=\"800-.4w%2B.8w=1400\"   DISABLED_style= \"max-width:90%; height:auto;\" >Rearrange:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.4w=600 ALIGN=MIDDLE  ALT=\".4w=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >Divide by .4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=1500 ALIGN=MIDDLE  ALT=\"w=1500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So m=2000-1500=500.  500 employees at Men's Mercantile and 1500 at Women's Wear. </SPAN>\n" );
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