document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119862>Question 1119862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need another question validated please.\r<BR>\n" );
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document.write( "Bill and Mary are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Bill sold 4 rolls of plain wrapping paper and 2 rolls of holiday wrapping paper for a total of $86. Mary sold 12 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for a total of $243. What is the cost each<BR>\n" );
document.write( "of one roll of plain wrapping paper and one roll of holiday wrapping paper?\r<BR>\n" );
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document.write( "What I did to solve:\r<BR>\n" );
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document.write( "Let x= represent price of plain wrapping paper<BR>\n" );
document.write( "Let y= represent price of holiday wrapping paper\r<BR>\n" );
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document.write( "4x + 2y = 86<BR>\n" );
document.write( "12x + 5y = 243\r<BR>\n" );
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document.write( "3(4x + 2y) = 3(86)<BR>\n" );
document.write( "-1(12x + 5y) = -1(243)\r<BR>\n" );
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document.write( "12x + 6y = 258<BR>\n" );
document.write( "-12x - 5y = 243<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "       1y = 15\r<BR>\n" );
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document.write( "4x + 2(15) = 86<BR>\n" );
document.write( "4x + 30 = 86<BR>\n" );
document.write( "4x + 30 - 30 = 86 - 30<BR>\n" );
document.write( "          4x = 56\r<BR>\n" );
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document.write( "          4x = 56<BR>\n" );
document.write( "          --   --<BR>\n" );
document.write( "          4     4\r<BR>\n" );
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document.write( "          x  = 14\r<BR>\n" );
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document.write( "The part that is throwing me of is 1y = 15. It doesn't seem right.\r<BR>\n" );
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document.write( "Thanks for your time.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735505 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10551)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Need another question validated please.\r<BR>\n" );
document.write( "\n" );
document.write( "Bill and Mary are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Bill sold 4 rolls of plain wrapping paper and 2 rolls of holiday wrapping paper for a total of $86. Mary sold 12 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for a total of $243. What is the cost each<BR>\n" );
document.write( "of one roll of plain wrapping paper and one roll of holiday wrapping paper?\r<BR>\n" );
document.write( "\n" );
document.write( "What I did to solve:\r<BR>\n" );
document.write( "\n" );
document.write( "Let x= represent price of plain wrapping paper<BR>\n" );
document.write( "Let y= represent price of holiday wrapping paper\r<BR>\n" );
document.write( "\n" );
document.write( "4x + 2y = 86<BR>\n" );
document.write( "12x + 5y = 243\r<BR>\n" );
document.write( "\n" );
document.write( "3(4x + 2y) = 3(86)<BR>\n" );
document.write( "-1(12x + 5y) = -1(243)\r<BR>\n" );
document.write( "\n" );
document.write( "12x + 6y = 258<BR>\n" );
document.write( "-12x - 5y = 243<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "       1y = 15\r<BR>\n" );
document.write( "\n" );
document.write( "4x + 2(15) = 86<BR>\n" );
document.write( "4x + 30 = 86<BR>\n" );
document.write( "4x + 30 - 30 = 86 - 30<BR>\n" );
document.write( "          4x = 56\r<BR>\n" );
document.write( "\n" );
document.write( "          4x = 56<BR>\n" );
document.write( "          --   --<BR>\n" );
document.write( "          4     4\r<BR>\n" );
document.write( "\n" );
document.write( "          x  = 14\r<BR>\n" );
document.write( "\n" );
document.write( "The part that is throwing me of is 1y = 15. It doesn't seem right.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks for your time.<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">You did everything correctly, and 1y = 15 is the same as y = 15. The coefficient on all variables without a noticeable coefficient is 1, OR,<BR>\n" );
document.write( "you can just easily DIVIDE each side by 1, as follows: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C5%2C+y%2C+%22=%22%2C+15%2F1%2C+%22=%22%2C+15%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C5%2C+y%2C+%22=%22%2C+15%2F1%2C+%22=%22%2C+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but that's taking it to the extreme because ANYTHING divided by 1 is ITSELF. </SPAN>\n" );
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