document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115404>Question 1115404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, appreciate your help please on solving this hard word problem below\r<BR>\n" );
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document.write( "Mr Jone works in a music shop in Nabua. Over the last three weeks there has been a sale, and music CDs in the Jumbo bin have been sold for $2, $5 or $10. One of Mr Jone’s customers bought a total of nine CDs. The total cost for buying the nine CDs was $60. The combined number of $2 and $5 CDs that the customer bought was twice as many as the number of $10 CDs that he bought.\r<BR>\n" );
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document.write( "i.	Set up the system of equations.<BR>\n" );
document.write( "ii.	Using Gauss Jordan Elimination Method, solve this system of equations to find the number of $10, $20, and $25 CDs that the customer bought.\r<BR>\n" );
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document.write( "Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730265 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=730265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of 2 dollar cds.<BR>\n" );
document.write( "let y = the number of 5 dollar cds.<BR>\n" );
document.write( "let z = the number of 10 dollar cds.\r<BR>\n" );
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document.write( "your first 2 equations are:\r<BR>\n" );
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document.write( "x + y + z = 9\r<BR>\n" );
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document.write( "2x + 5y + 10z = 60\r<BR>\n" );
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document.write( "you are given that the number of 2 and 5 dollar cds that the customer bought was 2 times the number of 10 dollar cds.\r<BR>\n" );
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document.write( "your third equation is x + y = 2z\r<BR>\n" );
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document.write( "subtract 2z from both sides of this equation to get x + y - 2z = 0\r<BR>\n" );
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document.write( "your 3 equations, now set up for matrix operations, are:\r<BR>\n" );
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document.write( "x + y + z = 9<BR>\n" );
document.write( "2x + 5y + 10z = 60<BR>\n" );
document.write( "x + y - 2z = 0\r<BR>\n" );
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document.write( "your matrix becomes:\r<BR>\n" );
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document.write( "              1       1      1      9\r\n" );
document.write( "              2       5      10     60\r\n" );
document.write( "              1       1     -2      0\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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document.write( "i used an online gauss jordan calculator to get you the answer.\r<BR>\n" );
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document.write( "the answer is:\r<BR>\n" );
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document.write( "x = 0<BR>\n" );
document.write( "y = 6<BR>\n" );
document.write( "z = 3\r<BR>\n" );
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document.write( "the gauss jordan calculator that i used can be found at:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.gregthatcher.com/Mathematics/GaussJordan.aspx\" target = \"_blank\">http://www.gregthatcher.com/Mathematics/GaussJordan.aspx</a>\r<BR>\n" );
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document.write( "the results from my use of this calculator are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/042101.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/042102.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/042103.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "while this was done by use of a calculator, the steps involved in arriving at the answer are also shown and you can duplicate them manually if you so desire.\r<BR>\n" );
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document.write( "this problem could also have been solved without using the gauss jordan calculator or the matrix method as follows:\r<BR>\n" );
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document.write( "your 3 equations that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "x + y + z = 9\r<BR>\n" );
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document.write( "2x + 5y + 10z = 60\r<BR>\n" );
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document.write( "x + y = 2z\r<BR>\n" );
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document.write( "in the first equation, replace x + y with 2z to get 2z + z = 9\r<BR>\n" );
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document.write( "solve for z to get z = 3\r<BR>\n" );
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document.write( "in the first equation, replace z with 3 to get x + y + 3 = 9\r<BR>\n" );
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document.write( "solve for x + y to get x + y = 6\r<BR>\n" );
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document.write( "solve for x to get x = 6 - y\r<BR>\n" );
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document.write( "in the second equation, replace z with 3 and replace x with 6 - y to get:\r<BR>\n" );
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document.write( "2x + 5y + 10z = 60 becomes 2 * (6 - y) + 5y + 30 = 60\r<BR>\n" );
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document.write( "simplify to get 12 - 2y + 5y + 30 = 60\r<BR>\n" );
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document.write( "combine like terms to get 42 + 3y = 60\r<BR>\n" );
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document.write( "subtract 42 from  both sides to get 3y = 18\r<BR>\n" );
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document.write( "solve for y to get y = 6.\r<BR>\n" );
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document.write( "since y = 6 and x + y = 6, then x has to be equal to 0.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x = 0<BR>\n" );
document.write( "y = 6<BR>\n" );
document.write( "z = 3\r<BR>\n" );
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document.write( "this is the same answer that gauss jordan calculator gave you, as it should.\r<BR>\n" );
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document.write( "your solutions is:\r<BR>\n" );
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document.write( "he 0 two dollar cds and 6 five dollar cds and 3 ten dollar cds.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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