document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24026>Question 24026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Kelly bought 3 pens and 4 pencils that cost 7.42 and Bill bought 4 pens and 5 pencils that cost 9.62 what is the cost of one pen and one pencil </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12693 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = cost of 1 pen<BR>\n" );
document.write( "y = cost of 1 pencil\r<BR>\n" );
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document.write( "3x+4y = 7.42<BR>\n" );
document.write( "4x+5y = 9.62\r<BR>\n" );
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document.write( "You have two equations and two variables, and I think the easiest way to solve this is to eliminate either the x or y coefficients.  The x coefficients are smaller, so find the common multiple of 3 and 4.  In other words, what number can you find that both 3 and 4 divide evenly into?  Answer is 12.  To get a 12 for the first equation, multiply both sides of the first equation by 4, and the second equation by 3.  Also, multiply both sides of the second equation by -1, to make it a +12x and a -12x, which will subtract out:\r<BR>\n" );
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document.write( "3x+4y = 7.42<BR>\n" );
document.write( "4x+5y = 9.62\r<BR>\n" );
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document.write( "4*(3x+4y) = 4*(7.42)<BR>\n" );
document.write( "-3*(4x+5y) = -3*(9.62)\r<BR>\n" );
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document.write( "12x + 16y = 29.68<BR>\n" );
document.write( "-12x - 15y = -28.86\r<BR>\n" );
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document.write( "Add these two equations together, and the x terms subtract out:<BR>\n" );
document.write( "1y =  .82<BR>\n" );
document.write( "y = $.82\r<BR>\n" );
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document.write( "Now, go back to the first equation and substitute this value for y:\r<BR>\n" );
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document.write( "3x+4*.82 = 7.42<BR>\n" );
document.write( "3x + 3.28 = 7.42<BR>\n" );
document.write( "3x +3.28 = 7.42- 3.28<BR>\n" );
document.write( "3x = 4.14\r<BR>\n" );
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document.write( "Divide both sides by 3:<BR>\n" );
document.write( "x= $1.38\r<BR>\n" );
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document.write( "Check this answer by substituting both values in the second equation:\r<BR>\n" );
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document.write( "4x+5y = 9.62<BR>\n" );
document.write( "4*1.38+5*.82 = 9.62<BR>\n" );
document.write( "$5.52 + 4.10 = 9.62<BR>\n" );
document.write( "It checks!\r<BR>\n" );
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document.write( "R^2 at SCC\r<BR>\n" );
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document.write( " </SPAN>\n" );
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