document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110556>Question 1110556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack and Jill spent two weeks touring Boston, New York, Philly, and Washington. They paid $120, $200, $80, and $100 per night respectively. Their total bill was 2020. The number of days spent in NYC was the same as the sum of the days spent in Boston and DC. They spent three times as many days in NYC as they did in Philly. How many days did they stay in each city?<BR>\n" );
document.write( "It says to answer the question using a 4x4 system of equations. I can't think of how to even start this :/  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725558 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2BN%2BP%2BW+=+14 ALIGN=MIDDLE  ALT=\"B%2BN%2BP%2BW+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total number of days was 14 (two weeks)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120B%2B200N%2B80P%2B100W+=+2020 ALIGN=MIDDLE  ALT=\"120B%2B200N%2B80P%2B100W+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total cost for lodging was $2020<BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+B%2BW ALIGN=MIDDLE  ALT=\"N+=+B%2BW\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the number of days spent in NYC was the same as the sum of the days spent in Boston and DC<BR>\n" );
document.write( "(4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+3P ALIGN=MIDDLE  ALT=\"N+=+3P\"   DISABLED_style= \"max-width:90%; height:auto;\" >  they spent three times as many days in NYC as they did in Philly<br><BR>\n" );
document.write( "Four equations, four unknowns.<br><BR>\n" );
document.write( "With 4 equations in 4 variables, there are always many different ways to find the answer.  Here is what I did....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120B%2B200N%2B80P%2B100W+=+2020 ALIGN=MIDDLE  ALT=\"120B%2B200N%2B80P%2B100W+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100B%2B100W%29%2B%28200N%29%2B80P%2B20B+=+2020 ALIGN=MIDDLE  ALT=\"%28100B%2B100W%29%2B%28200N%29%2B80P%2B20B+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" >  I separated the 120B into 100B+20B so I could use equation (3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100N%2B200N%2B80P%2B20B+=+2020 ALIGN=MIDDLE  ALT=\"100N%2B200N%2B80P%2B20B+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300N%2B80P%2B20B+=+2020 ALIGN=MIDDLE  ALT=\"300N%2B80P%2B20B+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900P%2B80P%2B20B+=+2020 ALIGN=MIDDLE  ALT=\"900P%2B80P%2B20B+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=980P%2B20B+=+2020 ALIGN=MIDDLE  ALT=\"980P%2B20B+=+2020\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With this equation (5), knowing that B, N, P, and W are whole numbers less than 14, there is only one possible value for P: P=2.  Then it follows immediately that B=3.  Equation (4) then gives N=6; and equation (1) then gives W=3.<br><BR>\n" );
document.write( "Answer: Philly 2, Boston 3, New York 6, Washington DC 3. </SPAN>\n" );
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