document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169940>Question 169940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Totally confused! Please help! Many Thanks!<BR>\n" );
document.write( "At a local garage sale, Chris bought 4 gardening magazines and 3 mugs for $8.70. Sarah bought 5 magazines, 2 mugs and 3 refrigerator magnets for $12.35. Steve bought 2 magazines, 4 mugs and 4 refrigerator magnets for $15.50. What was the price of each refrigerator magnet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125404 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=125404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At a local garage sale, Chris bought 4 gardening magazines and 3 mugs for $8.70. Sarah bought 5 magazines, 2 mugs and 3 refrigerator magnets for $12.35. Steve bought 2 magazines, 4 mugs and 4 refrigerator magnets for $15.50. What was the price of each refrigerator magnet?<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "GM = price of magazines<BR>\n" );
document.write( "MU = price of mugs<BR>\n" );
document.write( "RM = price of magnets<BR>\n" );
document.write( "4GM + 3MU = 870<BR>\n" );
document.write( "5GM + 2MU + 3RM = 1235<BR>\n" );
document.write( "2GM + 4MU + 4RM = 1550<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "It's 3 eqns in 3 unknowns.<BR>\n" );
document.write( "There are several ways to solve this.  I have an Excel sheet that does determinants, so I'll use that.<BR>\n" );
document.write( "| 4 3 0 870  |<BR>\n" );
document.write( "| 5 2 3 1235 | = 0<BR>\n" );
document.write( "| 2 4 4 1550 |<BR>\n" );
document.write( "Det = 4*(8-12) - 3*(20-6) = -16 - 42<BR>\n" );
document.write( "Det = -58<BR>\n" );
document.write( "Det*GM = 3*(3*1550 - 4*1235) + 870*(2*4-4*3)<BR>\n" );
document.write( "Det*GM = 3*(-290) + 870*(-4)<BR>\n" );
document.write( "Det*GM = -4350<BR>\n" );
document.write( "GM = -4350/(-58)<BR>\n" );
document.write( "GM = 75 (cents)<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Sub 75 into the 1st eqn to get MU<BR>\n" );
document.write( "4GM + 3MU = 870<BR>\n" );
document.write( "300 + 3MU = 870<BR>\n" );
document.write( "MU = 190<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Sub GM and MU<BR>\n" );
document.write( "2GM + 4MU + 4RM = 1550<BR>\n" );
document.write( "150 + 760 + 4RM = 1550<BR>\n" );
document.write( "4RM = 640<BR>\n" );
document.write( "RM = 160<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Magazine = $0.75<BR>\n" );
document.write( "Mug = $1.90<BR>\n" );
document.write( "Magnet = $1.60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );