document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150714>Question 150714</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello E-Tutors:)\r<BR>\n" );
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document.write( "Could someone lead me in the right direction with this college<BR>\n" );
document.write( "system of equations and inequality problem? The text book shows <BR>\n" );
document.write( "how to solve something similiar but it only displays an equation<BR>\n" );
document.write( "with two variables. Whereas this problem contains three variables.<BR>\n" );
document.write( "That throws me for a loop.\r<BR>\n" );
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document.write( "Problem: The students from algebra class go for coffee together <BR>\n" );
document.write( "every day. On Monday, Jordan paid $5.45 for three cartons of milk,<BR>\n" );
document.write( "four cups of coffee, and seven doughnuts. On Tuesday, Ryan paid $5.30<BR>\n" );
document.write( "for four milks, two coffees, and eight doughnuts. On Wednesday, Zack<BR>\n" );
document.write( "paid $5.15 for two milks, five coffees, and six doughnuts. \r<BR>\n" );
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document.write( "1.  Set up a system of equations to model this scenario.\r<BR>\n" );
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document.write( "I think this is right, but have no idea how to solve three layers, <BR>\n" );
document.write( "with 3 different variables.<BR>\n" );
document.write( "m=milk<BR>\n" );
document.write( "c=coffee<BR>\n" );
document.write( "d=doughnut\r<BR>\n" );
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document.write( "3m + 4c + 7d = 5.45<BR>\n" );
document.write( "4m + 2c + 8d = 5.30<BR>\n" );
document.write( "2m + 5c + 6d = 5.15\r<BR>\n" );
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document.write( "2.  Determine the cost of one carton milk, one coffee, and one doughnut<BR>\n" );
document.write( "by solving they system.\r<BR>\n" );
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document.write( "3. If on Thursday, Taylor had to pay for five milks, two coffees, and nine <BR>\n" );
document.write( "doughnuts how much did he spend?\r<BR>\n" );
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document.write( "Think, I can get this one if I learn how to solve the second question.\r<BR>\n" );
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document.write( "Thank you in advance for sharing your valuable skills with us,<BR>\n" );
document.write( "mishap mathematicians. :0)\r<BR>\n" );
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document.write( "Grateful,<BR>\n" );
document.write( "Jai\r<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 #110641 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3m + 4c + 7d = 5.45<BR>\n" );
document.write( "4m + 2c + 8d = 5.30<BR>\n" );
document.write( "2m + 5c + 6d = 5.15 <BR>\n" );
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document.write( "subtract 3rd equation from 1st to get:<BR>\n" );
document.write( " m -  c +  d = 0.30<BR>\n" );
document.write( "4m + 2c + 8d = 5.30<BR>\n" );
document.write( "2m + 5c + 6d = 5.15 <BR>\n" );
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document.write( "subtract 4 times 1st from 2nd; <BR>\n" );
document.write( "subtract 2 times 1st from 3rd:<BR>\n" );
document.write( " m -  c +  d = 0.30<BR>\n" );
document.write( " 0 + 6c + 4d = 4.10<BR>\n" );
document.write( " 0 + 7c + 4d = 4.55<BR>\n" );
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document.write( "interchange 2nd and 3rd to get:<BR>\n" );
document.write( "m -  c +  d = 0.30<BR>\n" );
document.write( "0 + 7c + 4d = 4.55<BR>\n" );
document.write( "0 + 6c + 4d = 4.10<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "subtract 3rd from 2nd to get:<BR>\n" );
document.write( "m -  c +  d = 0.30<BR>\n" );
document.write( "0 +  c +  0 = 0.45<BR>\n" );
document.write( "0 + 6c + 4d = 4.10<BR>\n" );
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document.write( "At this point you can see that c = 0.45<BR>\n" );
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document.write( "Subtitute that into the 3rd equation to solve for \"d\":<BR>\n" );
document.write( "6(0.45) + 4d = 4.10<BR>\n" );
document.write( "2.7 + 4d = 4.10<BR>\n" );
document.write( "4d = 1.40 <BR>\n" );
document.write( "d = 0.35<BR>\n" );
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document.write( "Substitute the values of c and d into the 1st equation to solve for \"m\":<BR>\n" );
document.write( "m - 0.45 + 0.35 = 0.30<BR>\n" );
document.write( "m - 0.10 = 0.30<BR>\n" );
document.write( "m = 0.40<BR>\n" );
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document.write( "one mild costs 40 cents<BR>\n" );
document.write( "one coffee costs 45 cents<BR>\n" );
document.write( "one doughnut costs 35 cents<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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