document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162245>Question 1162245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kelly has a collection of nickels, dimes, and quarters with a total value of $6.10. There are four more nickels than dimes and twice as many quarters as nickels. How many of each coin is in her collection? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786000 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=786000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Take the time to set up the problem using a single variable.  Blindly plunging into solving the problem using three variables will make more work for you.<br><BR>\n" );
document.write( "The given information compares nickels to dimes and quarters to nickels.  That is a clue that almost certainly it will be easiest to set up the problem using the number of nickels as the variable.<br><BR>\n" );
document.write( "x = number of nickels<BR>\n" );
document.write( "x-4 = number of dimes  [the number of nickels is 4 more than the number of dimes]<BR>\n" );
document.write( "2x = number of quarters  [there are twice as many quarters as nickels]<br><BR>\n" );
document.write( "The total value is $6.10, or 610 cents:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%282x%29%2B10%28x-4%29%2B5%28x%29+=+610 ALIGN=MIDDLE  ALT=\"25%282x%29%2B10%28x-4%29%2B5%28x%29+=+610\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50x%2B10x-40%2B5x+=+610 ALIGN=MIDDLE  ALT=\"50x%2B10x-40%2B5x+=+610\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65x+=+650 ALIGN=MIDDLE  ALT=\"65x+=+650\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10 ALIGN=MIDDLE  ALT=\"x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER:<BR>\n" );
document.write( "nickels: x = 10<BR>\n" );
document.write( "dimes: x-4 = 6<BR>\n" );
document.write( "quarters: 2x = 20<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "10(5)+6(10)+20(25) = 50+60+500 = 610<br><BR>\n" );
document.write( "Solving problems like this using mental arithmetic and logical reasoning can be good mental exercise.  It might go something like this:<br><BR>\n" );
document.write( "Loan Kelly 4 more dimes, so that the numbers of nickels and dimes are the same.  The total value is now 610+40 = 650.<br><BR>\n" );
document.write( "The coins now consist of a number of nickels, an equal number of dimes, and twice that many quarters.  A group of one nickel, one dime, and two quarters together has a value of 65 cents.<br><BR>\n" );
document.write( "Since the new total value of the coins is 650 cents, that must mean there are 10 of those groups -- making 10 nickels, 10 dimes, and 20 quarters.<br><BR>\n" );
document.write( "Now have Kelly give you back the 4 dimes you loaned her, to find that the coins she has are 10 nickels, 6 dimes, and 20 quarters.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );