document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1095807>Question 1095807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve using substitution method<BR>\n" );
document.write( "For 2000 dollars are bought 15 notebooks and 12 markers. How much does 1 notebook and much does 1 marker cost, if 3 markers cost as much as 6 notebooks?\r<BR>\n" );
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document.write( "solving looks something like <BR>\n" );
document.write( "12x+15y=2000<BR>\n" );
document.write( "6y=3x\r<BR>\n" );
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document.write( "Please explain thoroughly and step by step :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710301 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=710301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you buy 15 notebooks and 12 markers for 2000.\r<BR>\n" );
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document.write( "how much does 1 notebook and 1 marker cost, if 3 markers cost as much as 6 notebooks.\r<BR>\n" );
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document.write( "let x equal the price of a notebook.<BR>\n" );
document.write( "let y equal the price of a marker.\r<BR>\n" );
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document.write( "15x + 12y = 2000\r<BR>\n" );
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document.write( "this equation says that 15 times the price of a notebook plus 12 times the price of a marker is equal to 2000 dollars.\r<BR>\n" );
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document.write( "3 markers cost as much as 6 notebooks.\r<BR>\n" );
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document.write( "3y = 6x\r<BR>\n" );
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document.write( "this equation says that 3 times the price of a marker is equal to 6 times the price of a notebook.\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "15x + 12y = 2000<BR>\n" );
document.write( "3y = 6x\r<BR>\n" );
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document.write( "when you solve by substitution, you solve for one of the variables in one of the equations and then use that value in the other equationm.\r<BR>\n" );
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document.write( "either equation will do.\r<BR>\n" );
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document.write( "i'll use the first equation to solve for y.\r<BR>\n" );
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document.write( "start with 15x + 12y = 2000<BR>\n" );
document.write( "subtract 15x from both sides of the equation to get 12y = 2000 - 15x<BR>\n" );
document.write( "divide both sides of the equation by 15 to get y = (2000 - 15x) / 12\r<BR>\n" );
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document.write( "use that value for y in the second equation.\r<BR>\n" );
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document.write( "start with 3y = 6x<BR>\n" );
document.write( "replace y to get 3 * (2000 - 15x) / 12 = 6x.<BR>\n" );
document.write( "divide both sides of the equation by 3 to get (2000 - 15x) / 12 = 2x.<BR>\n" );
document.write( "multiply both sides of the equation by 12 to get 2000 - 15x = 24x.<BR>\n" );
document.write( "add 15x to both sides of the equation to get 2000 = 39x.<BR>\n" );
document.write( "divide both sides of the equation by 39 to get 2000 / 39 = x.<BR>\n" );
document.write( "solve for x to get x = 2000 / 39 = 51.28205128.\r<BR>\n" );
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document.write( "go back to the original equation of 15x + 12y = 2000 and replace x with the value that you calculated for it.\r<BR>\n" );
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document.write( "you will get 15 * 51.28205128 + 12y = 2000<BR>\n" );
document.write( "solve for y to get y = (2000 - 15 * 51.28205128) / 12.<BR>\n" );
document.write( "result is y = 102.5641026\r<BR>\n" );
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document.write( "go back to both original equaitons and see if they're true when you replace x and y with their calculated values.\r<BR>\n" );
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document.write( "3y = 6x becomes 3*102.5641026 = 6*51.28205128<BR>\n" );
document.write( "result is 3076923077 = 307.6923077 which confirms this equation is good.\r<BR>\n" );
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document.write( "15x + 12y = 2000 becomes 15*51.28205128 + 12*102.5641026.<BR>\n" );
document.write( "result is 2000 = 200 which confirms this equation is also good.\r<BR>\n" );
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document.write( "you probably want to round your numbers to the nearest penny.\r<BR>\n" );
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document.write( "therefore, your solution should be:\r<BR>\n" );
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document.write( "x = 51.28<BR>\n" );
document.write( "y = 202.56\r<BR>\n" );
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document.write( "if you try to confirm with these rounded numbers, you won't be exactly right because of the rounding.\r<BR>\n" );
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document.write( "you need to use the un-rounded numbers for your confirmation.\r<BR>\n" );
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document.write( "note that i had:\r<BR>\n" );
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document.write( "15x + 12y = 2000<BR>\n" );
document.write( "3y = 6x\r<BR>\n" );
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document.write( "and you had:\r<BR>\n" );
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document.write( "12x+15y=2000<BR>\n" );
document.write( "6y=3x \r<BR>\n" );
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document.write( "it looks to me like i was using x as the price of a notebook and you were using x as the price of a marker.\r<BR>\n" );
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document.write( "replace your x with y and you y with x and we're the same.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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