document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110439>Question 1110439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack and Jill spent two weeks touring Boston, New York City, Philadelphia, and Washington D.C. 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 D.C. 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( "a) answer question using a combination of algebra and logic.<BR>\n" );
document.write( "b) answer the question again using a 4x4 system of equations.\r<BR>\n" );
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document.write( "Does this mean there's another way to do this without a system of equations? That's the only way I can think of doing it. I just know that 120B+200N+80P+100W=2020.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725556 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Jack and Jill spent two weeks touring Boston, New York City, Philadelphia, and Washington D.C.<BR>\n" );
document.write( "let b, n, p, and w = the no. of days in each season, write an equation for each statement<BR>\n" );
document.write( ":<BR>\n" );
document.write( " They paid $120,$200,$80, and $100 per night respectively.<BR>\n" );
document.write( " Their total bill was $2020.<BR>\n" );
document.write( "120b + 200n + 80p + 100w = 2020<BR>\n" );
document.write( "Simplify, divide by 20<BR>\n" );
document.write( "6b + 10n + 4p + 5w = 201<BR>\n" );
document.write( ":<BR>\n" );
document.write( " The number of days spent in NYC was the same as the sum of the days spent in Boston and D.C.<BR>\n" );
document.write( "n = b + w<BR>\n" );
document.write( "or<BR>\n" );
document.write( "b = n - w<BR>\n" );
document.write( ":<BR>\n" );
document.write( " They spent three times as many days in NYC as they did in Philly.<BR>\n" );
document.write( "n = 3p<BR>\n" );
document.write( "or<BR>\n" );
document.write( "p = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2F3 ALIGN=MIDDLE  ALT=\"n%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "a) answer question using a combination of algebra and logic.<BR>\n" );
document.write( "Substitute in the 1st equation, for b & p<BR>\n" );
document.write( "6(n-w) + 10n + 4(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2F3 ALIGN=MIDDLE  ALT=\"n%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5w = 101<BR>\n" );
document.write( "get rid of the fraction, multiply thru b 3<BR>\n" );
document.write( "18(n-w) + 30n + 4n + 15w = 303<BR>\n" );
document.write( "18n - 18w + 30n + 4n + 15w = 303<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "52n - 3w = 303<BR>\n" );
document.write( "have 4 unknowns and only 3 equations, but we know they have to be integers<BR>\n" );
document.write( "Write an equation we can enter into a graphing calc<BR>\n" );
document.write( "3w = 52n - 303<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2852n-303%29%2F3 ALIGN=MIDDLE  ALT=\"%2852n-303%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%2F3 ALIGN=MIDDLE  ALT=\"52%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >n - 101<BR>\n" );
document.write( "table reveals only one integer solution that makes sense<BR>\n" );
document.write( "n = 6, w = 3<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "p = 6/3 = 2 days<BR>\n" );
document.write( "b = 6 - 3 = 3 days<BR>\n" );
document.write( ":<BR>\n" );
document.write( "How many days did they stay in each city? <BR>\n" );
document.write( "Boston 3 days, New York 6 days, Philly 2 days and Wash 3 days<BR>\n" );
document.write( "see if that works<BR>\n" );
document.write( "120(3) + 200(6) + 2(80) + 100(3) = 2020<BR>\n" );
document.write( ":<BR>\n" );
document.write( " b) answer the question again using a 4x4 system of equations.<BR>\n" );
document.write( "I don't know either,  how you could do this with a 4 by 4 matrix  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );