document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=292028>Question 292028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1st question-  If four times a number added to 3 is divided by the number plus 8, the result is seven halves. find the number.<BR>\n" );
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document.write( "2nd question- One custodian cleans a suite of offices in 5 hours. When a second worker is asked to join the regular custodian, the job takes only 2 1/2 hours. How long does it take the second worker to do the same job alone?\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211041 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If four times a number added to 3 is divided by the number plus 8, the result is seven halves. find the number.\r<BR>\n" );
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document.write( "Let's break it down in parts.\r<BR>\n" );
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document.write( "4 times a number: 4x<BR>\n" );
document.write( "added to 3: 4x+3<BR>\n" );
document.write( "Divided by the number plus 8: (4x+3)/(x+8)\r<BR>\n" );
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document.write( "And it's equal to 7 halves, or 7/2\r<BR>\n" );
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document.write( "Putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B3%29%2F%28x%2B8%29+=+7%2F2 ALIGN=MIDDLE  ALT=\"%284x%2B3%29%2F%28x%2B8%29+=+7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First multiply both sides by x+8.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B3%29+=+7%28x%2B8%29%2F2 ALIGN=MIDDLE  ALT=\"%284x%2B3%29+=+7%28x%2B8%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then multiply both sides by 2. (this is called cross-multiply)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%284x%2B3%29+=+7%28x%2B8%29 ALIGN=MIDDLE  ALT=\"2%284x%2B3%29+=+7%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "8x+6=7x+56<BR>\n" );
document.write( "x=50\r<BR>\n" );
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document.write( "For your second question,\r<BR>\n" );
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document.write( "the first custodian's rate = 1 suite/5 hours<BR>\n" );
document.write( "the second custodian's rate = x suites/5 hours \r<BR>\n" );
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document.write( "their combined rate of work = 1 suite/2.5 hours\r<BR>\n" );
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document.write( "(First custodian's work rate) + (second custodian's work rate) = combined work rate\r<BR>\n" );
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document.write( "1/5 + x/5  = 1/2.5\r<BR>\n" );
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document.write( "Rearrange this for x and you'll find that x=1, meaning that the second custodian's work rate is the same as the first's, 1 suite/5 hours. It would take him the same amount of time as the first custodian. </SPAN>\n" );
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