document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120158>Question 1120158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a local garage sale, Christ bought 4 gardening magazines and 3 mugs for $8.70; Sarah bought 5 magazines , 2 mugs and 3 refrigerator magnets for $12.35; and Steve bought 2 magazines, 4 ceramic 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 #735849 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=735849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Yes, there are ways to solve systems of equations using calculators of various sorts.  But solving them with pencil and paper is a useful skill....<br><BR>\n" );
document.write( "The statement of the problem yields three equations:<BR>\n" );
document.write( "(1) 4x+3y = 8.70<BR>\n" );
document.write( "(2) 5x+2y+3z = 12.35<BR>\n" );
document.write( "(3) 2x+4y+4z = 15.50<br><BR>\n" );
document.write( "Since one of the equations has only two of the variables, very probably the best way to start solving the system is to eliminate the third variable from the other two equations, yielding a system of two equation in two unknowns.<br><BR>\n" );
document.write( "20x+8y+12z = 49.40<BR>\n" );
document.write( "6x+12y+12z = 46.50<BR>\n" );
document.write( "14x-4y = 2.90<br><BR>\n" );
document.write( "Now eliminate y between this equation and equation (1).<br><BR>\n" );
document.write( "16x+12y = 34.80<BR>\n" );
document.write( "42x-12y = 8.70<BR>\n" );
document.write( "58x = 43.50<BR>\n" );
document.write( "x = 43.50/58 = 0.75<br><BR>\n" );
document.write( "4(.75)+3y = 8.70<BR>\n" );
document.write( "3y = 5.70<BR>\n" );
document.write( "y = 1.90<br><BR>\n" );
document.write( "2(.75)+4(1.90)+4z = 15.50<BR>\n" );
document.write( "4z = 6.40<BR>\n" );
document.write( "z = 1.60<br><BR>\n" );
document.write( "The cost of each refrigerator magnet, z, was $1.60.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );