document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181953>Question 1181953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alice stopped by a coffee shop two days in a row at a conference to buy drinks and<BR>\n" );
document.write( "pastries. On the first day, she bought a cup of coffee and two muffins for which she<BR>\n" );
document.write( "paid |6.87. The next day she bought two cups of coffee and three muffins (for herself<BR>\n" );
document.write( "and a friend). Her bill was |11.25. Use the method of elimination to determine the<BR>\n" );
document.write( "price of a cup of coffee, and the price of a muffin. Clearly explain your set-up for the<BR>\n" );
document.write( "problem<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 #811925 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is a different path to the solution.  Not the most efficient path; but if you are good with mental arithmetic this method can allow you to solve the problem mentally.<br><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "2 cups of coffee and 3 muffins cost $11.25 : 2x+3y=11.25 [1]<BR>\n" );
document.write( "1 cup of coffee and 2 muffins cost $6.87 : x+2y=6.87 [2]<br><BR>\n" );
document.write( "Comparing those two purchases tells us<br><BR>\n" );
document.write( "1 cup of coffee and 1 muffin cost $11.25-$6.87 = $4.38 : x+y=4.38 [3]<br><BR>\n" );
document.write( "Now use elimination using [2] and [3]: multiply [3] by -1 and add to [2] to give<br><BR>\n" );
document.write( "y=6.87-4.38=2.49 [4]<br><BR>\n" );
document.write( "Then use [3] and [4] to find x=4.38-2.49=1.89<br><BR>\n" );
document.write( "ANSWERS: coffee x=$1.89; muffin y=$2.49<br><BR>\n" );
document.write( "Mentally, the solution goes something like this:<br><BR>\n" );
document.write( "2 coffees and 3 muffins cost $11.25<BR>\n" );
document.write( "1 coffee and 2 muffins cost $6.87<BR>\n" );
document.write( "So 1 less coffee and 1 less muffin costs $11.25=$6.87=$4.38 less<BR>\n" );
document.write( "Taking away 1 coffee and 1 muffin again leaves one muffin, at a cost of $6.87-$4.38=$2.49<BR>\n" );
document.write( "Then the cost of the coffee is $4.38-$2.49=$1.89<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );