document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548227>Question 548227</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a system of equation problem and I am not sure what I need to do as we are just starting them.  Could you please help me out? The question is How many days before 17th August is it, if 50 days ago it was four times as many since March 30th?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #356840 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=356840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The other tutor made an error, noticed it and quit, which tutors\r\n" );
document.write( "should not do.\r\n" );
document.write( "\r\n" );
document.write( "The problem is:\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "How many days before August 17 is \"today\", if 50 days ago \"today\"<BR>\n" );
document.write( "it was four times that many days since March 30th? <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "You need a date number list like the one below.  This one is for a \r\n" );
document.write( "non-leap year, but you can put in Feb. 29, like we will have in 2012\r\n" );
document.write( "if you like.  It will just make the date numbers come out one less.\r\n" );
document.write( "But the answer will be the same, since, luckily, all the dates are\r\n" );
document.write( "after February.\r\n" );
document.write( "\r\n" );
document.write( " 1. January 1\r\n" );
document.write( " 2. January 2\r\n" );
document.write( " 3. January 3\r\n" );
document.write( " 4. January 4\r\n" );
document.write( " 5. January 5\r\n" );
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document.write( " 8. January 8\r\n" );
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document.write( "15. January 15\r\n" );
document.write( "16. January 16\r\n" );
document.write( "17. January 17\r\n" );
document.write( "18. January 18\r\n" );
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document.write( "152. June 1\r\n" );
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document.write( "180. June 29\r\n" );
document.write( "181. June 30\r\n" );
document.write( "182. July 1\r\n" );
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document.write( "213. August 1\r\n" );
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document.write( "229. August 17\r\n" );
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document.write( "305. November 1\r\n" );
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document.write( "334. November 30\r\n" );
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document.write( "364. December 30\r\n" );
document.write( "365. December 31\r\n" );
document.write( "\r\n" );
document.write( "Let's let x = the date number of \"today\" (or, rather, the date we are\r\n" );
document.write( "PRETENDING is \"today\" for this problem) \r\n" );
document.write( "\r\n" );
document.write( "Let's let y = the number of days from \"today\" until August 17th.\r\n" );
document.write( "\r\n" );
document.write( "We have four dates to consider:\r\n" );
document.write( "\r\n" );
document.write( "\"Today\", which is date number x\r\n" );
document.write( "March 30, which was date number 89.\r\n" );
document.write( "50 days ago \"today\", which was date number x-50\r\n" );
document.write( "August 17, which is date #229\r\n" );
document.write( "\r\n" );
document.write( "So we have:\r\n" );
document.write( "\r\n" );
document.write( "(Today) + (y days) = (August 17)\r\n" );
document.write( "\r\n" );
document.write( "That gives us the first equation:\r\n" );
document.write( "\r\n" );
document.write( "             x + y = 229  \r\n" );
document.write( "\r\n" );
document.write( "Which is already simplified. \r\n" );
document.write( "\r\n" );
document.write( "We must subtract 4 times as many days from (50 days ago) \r\n" );
document.write( "as \"today\" is before August 17 to get back to March 30.\r\n" );
document.write( "\r\n" );
document.write( "Therefore  \r\n" );
document.write( "\r\n" );
document.write( "(50 days ago) - (4 times y days) = (March 30)\r\n" );
document.write( "\r\n" );
document.write( "That gives us the equation:\r\n" );
document.write( "\r\n" );
document.write( "       (x-50) - 4y = 89   \r\n" );
document.write( "\r\n" );
document.write( "Simplifying that\r\n" );
document.write( "\r\n" );
document.write( "       x - 50 - 4y = 89\r\n" );
document.write( "            x - 4y = 139\r\n" );
document.write( "\r\n" );
document.write( "So the system of equations is\r\n" );
document.write( "\r\n" );
document.write( "            x  + y = 229\r\n" );
document.write( "            x - 4y = 139\r\n" );
document.write( "\r\n" );
document.write( "Solve the first equation for x\r\n" );
document.write( "\r\n" );
document.write( "            x  + y = 229\r\n" );
document.write( "                 x = 229 - y\r\n" );
document.write( "\r\n" );
document.write( "Substitute that for x in\r\n" );
document.write( "\r\n" );
document.write( "            x - 4y = 139\r\n" );
document.write( "    (229 - y) - 4y = 139\r\n" );
document.write( "      229 - y - 4y = 139\r\n" );
document.write( "          229 - 5y = 139\r\n" );
document.write( "               -5y = -90\r\n" );
document.write( "                 y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-90%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"%28-90%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "                 y = 18\r\n" );
document.write( "\r\n" );
document.write( "That's actually the answer, but to check it we\r\n" );
document.write( "must also find x, by substituting 18 for y in\r\n" );
document.write( "\r\n" );
document.write( "                 x = 229 - y\r\n" );
document.write( "                 x = 229 - 18\r\n" );
document.write( "                 x = 211\r\n" );
document.write( "\r\n" );
document.write( "So \"today\" is July 30, date #211.\r\n" );
document.write( "In 18 days from \"today\", it will be date #211 + 18 = #229,\r\n" );
document.write( "or August 17.  That checks.\r\n" );
document.write( "\r\n" );
document.write( "50 days ago from \"today\" was #211-50 = #161, or June 10.\r\n" );
document.write( "\r\n" );
document.write( "The number of days March 30 was before June 10 was #161-#89 or 72 days,\r\n" );
document.write( "\r\n" );
document.write( "It is 18 days from \"today\", July 30, until August 17, and since\r\n" );
document.write( "72 days is 4 times 18, then March 30 is 4 times as many days before\r\n" );
document.write( "June 10 as August 17 is from \"today\", July 30.\r\n" );
document.write( "\r\n" );
document.write( "So it checks.\r\n" );
document.write( "\r\n" );
document.write( "The answer is 18 days.  (If you use leap year date numbers, all the\r\n" );
document.write( "date numbers will be 1 less, but the answer will still be 18.\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );