document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65193>Question 65193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Will you please help me with this problem?\r<BR>\n" );
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document.write( "Write a system of two equations in two unknowns.  Solve the system by using the addition method. « Mike paid $2.98 for three doughnuts and two coffees.  The next day, he paid $1.64 for two doughnuts and one coffee.  How much does it cost for one doughnut and one coffee? \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45715 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=45715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Let x=cost of 1 doughnut<BR>\n" );
document.write( "And y=cost of 1 coffee\r<BR>\n" );
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document.write( "Now we are told that mike paid $2.98 for 3 doughnuts and 2 coffees\r<BR>\n" );
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document.write( "so 3x+2y=$2.98\r<BR>\n" );
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document.write( "Next day we are told that Mike paid $1.64 for 2 doughnuts and 1 coffee<BR>\n" );
document.write( "That would be 2x+y=$1.64\r<BR>\n" );
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document.write( "Now we have our two equations:\r<BR>\n" );
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document.write( "(1)  3x+2y=$2.98<BR>\n" );
document.write( "(2)  2x+y=$1.64 \r<BR>\n" );
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document.write( "Multiply Equation #(2) by (-2) and we get:\r<BR>\n" );
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document.write( "(2a) -4x-2y=-$3.28<BR>\n" );
document.write( "(1)   3x+2y=$2.98\r<BR>\n" );
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document.write( "Add (1) and (2a) and we get:<BR>\n" );
document.write( "-x=-$.30<BR>\n" );
document.write( "x=30 cents cost of 1 doughnut\r<BR>\n" );
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document.write( "substitute in (1) and we have:\r<BR>\n" );
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document.write( "3($.30)+2y=$2.98<BR>\n" );
document.write( "$.90+2y=$2.98  subtract $.90 from both sides:<BR>\n" );
document.write( "2y=$2.98-$.90<BR>\n" );
document.write( "2y=$2.08<BR>\n" );
document.write( "y=$1.04  cost of 1 coffee\r<BR>\n" );
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document.write( "ck substitute in (1)\r<BR>\n" );
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document.write( "3($.30)+2($1.04)=$2.98<BR>\n" );
document.write( "$.90+$2.08=$2.98<BR>\n" );
document.write( "$2.98=$2.98\r<BR>\n" );
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document.write( "Substitute in (2)<BR>\n" );
document.write( "2($.30)+$1.04=$1.64<BR>\n" );
document.write( "$.60+$1.04=$1.64<BR>\n" );
document.write( "$1.64=$1.64\r<BR>\n" );
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document.write( "Hope this helps.  Happy holidays.----ptaylor </SPAN>\n" );
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