document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60293>Question 60293</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534490247/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables.\r<BR>\n" );
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document.write( "Cindy has 43 coins consisting of nickels and dimes.  The total value of the coins is $3.40.  How many coins of each kind does she have?\r<BR>\n" );
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document.write( "I have gotten this far:<BR>\n" );
document.write( "n + d = 3.40<BR>\n" );
document.write( "is that right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41430 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=41430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This word problem has to do with coins, but I need to solve it by setting up and solving a system of two linear equations in two variables.\r<BR>\n" );
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document.write( "Cindy has 43 coins consisting of nickels and dimes.  The total value of the coins is $3.40.  How many coins of each kind does she have?<BR>\n" );
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document.write( "I like to do these in terms of cents to avoid decimals.<BR>\n" );
document.write( "Let number of nickles be:n<BR>\n" );
document.write( "Let the number of dimes be:d<BR>\n" );
document.write( "When we add the coins together we have 43 coins: n+d=43<BR>\n" );
document.write( "Nickels are worth 5 cents, so the amount of money in nickels we have is: 5n<BR>\n" );
document.write( "Dimes are worth 10 cents: 10d<BR>\n" );
document.write( "Total cents when added together: 5n+10d=340<BR>\n" );
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document.write( "E1:  n+d=43<BR>\n" );
document.write( "E2:  5n+10d=340<BR>\n" );
document.write( "Solve  E1, for one of the variables like d and substitute into E2 and solve for n.<BR>\n" );
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document.write( "E1: n+d=43 --> d=43-n<BR>\n" );
document.write( "5n+10(43-n)=340<BR>\n" );
document.write( "5n+430-10n=340<BR>\n" );
document.write( "-5n+430=340<BR>\n" );
document.write( "-5n+430-430=340-430<BR>\n" );
document.write( "-5n=-90<BR>\n" );
document.write( "-5n/-5=-90/-5<BR>\n" );
document.write( "n=18<BR>\n" );
document.write( "Substitute that into E1 to see how many dimes there were:<BR>\n" );
document.write( "d=43-18<BR>\n" );
document.write( "d=25<BR>\n" );
document.write( "There were 18 nickels and 25 dimes.<BR>\n" );
document.write( "Sanity Check: does 18 nickels and 25 dimes = $3.40?  You decide if we're right.<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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