document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122003>Question 1122003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Robin has a collection of nickels, dimes, and quarters worth $37.50. She has 30 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738049 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=738049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Of course, being able to set up and solve a problem like this using formal algebra is a useful skill.  But solving the problem using logical analysis can be good brain exercise.<br><BR>\n" );
document.write( "The number of quarters is twice the number of dimes; and the number of nickels is 30 less than the number of dimes.  The total value is $37.50.<br><BR>\n" );
document.write( "(1) Add 30 more nickels, so that the number of nickels is the same as the number of dimes.  The total value is now $37.50 + $1.50 = $39.<BR>\n" );
document.write( "(2) Now the numbers of dimes and nickels are the same, and the number of quarters is twice as much.  So make group of 2 quarters, 1 dime, and 1 nickel; each of those group has a value of $0.65.<BR>\n" );
document.write( "(3) The number of those groups needed to make the new total of $39 is 39/0.65 = 60.<BR>\n" );
document.write( "(4) So with the added 30 nickels, the collection has 120 quarters, 60 dimes, and 60 nickels.<BR>\n" );
document.write( "(5) Now take away the 30 nickels you added in the beginning to get the final answer:  120 quarters, 60 dimes, and 30 nickels.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "120(.25)+60(.10)+30(.05) = 30.00+6.00+1.50 = 37.50 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );