document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118506>Question 118506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. One half of a number is 3 more than one sisxth of the same number. What is the number?<BR>\n" );
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document.write( "2. The denominator of a certain fraction is three times the numerator. If one is added to the <BR>\n" );
document.write( "numerator and subtracted from the denominator, the result equals 1/2. Find the original fraction.<BR>\n" );
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document.write( "3. The denominator of a fraction is 5 more than the numerator. If 5 is added to the numerator and 2 is added to the denominator, the value of the fraction is 8/9. Find the original fraction.<BR>\n" );
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document.write( "4. The numerator is one less than the denominator. If two is added to the denominator and <BR>\n" );
document.write( "subtracted from the nomerator, the value of the fraction is 1/2. Find the original fraction.\r<BR>\n" );
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document.write( "5. Ed can do a job in four days. When Ed and Maymay work together, it would take them 2 1/3 days. <BR>\n" );
document.write( "How long would the job take Maymay to do it alone?<BR>\n" );
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document.write( "6. A cold water faucet could fill a sink in 15 minutes, and a hot water faucet can fill it in 12 <BR>\n" );
document.write( "minutes. The drain can empty the sink in 25 minutes. If both faucet are on and the drain is open,<BR>\n" );
document.write( "how long would it take to fill the sink?<BR>\n" );
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document.write( "7. Julius can paint a house three times faster than Ruben. Working together, they can paint a <BR>\n" );
document.write( "house in four days. How long would it take the faster painter if he works alone?<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 #86670 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=86670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It looks like you have put your entire homework assignment into one question.  This site was not created so that you could get someone to do your homework for you.  You have two different types of problems.  I'll show you how to do one of each.\r<BR>\n" );
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document.write( "1.  One half of a number is 3 more than one sixth of the same number. What is the number?\r<BR>\n" );
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document.write( "Let the number be x.  One half of the number is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2 ALIGN=MIDDLE  ALT=\"x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  One sixth of the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6 ALIGN=MIDDLE  ALT=\"x%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 3 more than that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F6%29%2B3 ALIGN=MIDDLE  ALT=\"%28x%2F6%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So you can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2=%28x%2F6%29%2B3 ALIGN=MIDDLE  ALT=\"x%2F2=%28x%2F6%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides by 6 to eliminate the denominators:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=x%2B18 ALIGN=MIDDLE  ALT=\"3x=x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract x from both sides to get the variable on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=18 ALIGN=MIDDLE  ALT=\"2x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check your answer:\r<BR>\n" );
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document.write( "Half of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One sixth of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F6=3%2F2 ALIGN=MIDDLE  ALT=\"9%2F6=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%2B3=%283%2F2%29%2B%286%2F2%29=9%2F2 ALIGN=MIDDLE  ALT=\"%283%2F2%29%2B3=%283%2F2%29%2B%286%2F2%29=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, answer checks\r<BR>\n" );
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document.write( "6. A cold water faucet could fill a sink in 15 minutes, and a hot water faucet can fill it in 12 minutes. The drain can empty the sink in 25 minutes. If both faucets are on and the drain is open, how long would it take to fill the sink?\r<BR>\n" );
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document.write( "If the cold faucet can fill the sink in 15 minutes, it fills <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >th of the sink in 1 minute.  Likewise, the hot faucet fills <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >th of the sink in 1 minute.  The LCD of 15 and 12 is 60, so the cold faucet fills the sink at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F60 ALIGN=MIDDLE  ALT=\"4%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute, and the hot at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F60 ALIGN=MIDDLE  ALT=\"5%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute.  Together, they fill the sink at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F60%29%2B%285%2F60%29=9%2F60 ALIGN=MIDDLE  ALT=\"%284%2F60%29%2B%285%2F60%29=9%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute.  Just as a sanity check, it would take 6 and 2/3 minutes to fill the sink IF the drain were CLOSED.\r<BR>\n" );
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document.write( "The drain empties the sink at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25 ALIGN=MIDDLE  ALT=\"1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the sink per minute.  Now we need an LCD for 25 and 60:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=5%2A5 ALIGN=MIDDLE  ALT=\"25=5%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=2%2A2%2A3%2A5 ALIGN=MIDDLE  ALT=\"60=2%2A2%2A3%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A3%2A5%2A5=300 ALIGN=MIDDLE  ALT=\"2%2A2%2A3%2A5%2A5=300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "With both faucets and the drain open fully, the sink is filling at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F300 ALIGN=MIDDLE  ALT=\"45%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F300 ALIGN=MIDDLE  ALT=\"12%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2F300 ALIGN=MIDDLE  ALT=\"33%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" >ths per minute.\r<BR>\n" );
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document.write( "The sink therefore fills in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F33=100%2F11 ALIGN=MIDDLE  ALT=\"300%2F33=100%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes exactly, or 9 minutes as a very close approximation (rounded from the repeating decimal 9.09...).  If you require a decimal answer (instead of a fraction), express it as 9 because you shouldn't give an answer that is more precise than the least precise measurement given in the problem.  The time measurements given were all in whole minutes, so your answer should be in whole minutes.\r<BR>\n" );
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document.write( "By the way, remember the sanity check.  6 and 2/3 minutes to fill if the drain were closed and 9 minutes with the drain open is a ratio of about 1.4.  45/300 with the drain closed and 33/300 to fill with the drain open is also a ratio of about 1.4.  That quick mental calculation assures us that the answer is reasonable.\r<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
document.write( "John<BR>\n" );
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