document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203989>Question 203989</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $42.35. If there were five times as many nickels as dimes how many of each coin does he have?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153911 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=153911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let n = number of nickels<BR>\n" );
document.write( "let d = number of dimes<BR>\n" );
document.write( "since a nickel is worth .05 and a dime is worth .1, then the total money you have is given by the equation:<BR>\n" );
document.write( ".05*n + .1*d = 42.35<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the number of nickels = 6 times the number of dimes, you can replace n with 5d in your equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( ".05*5d + .1*d = 42.35<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "d*(.05*5 + .1) = 42.35 which becomes .35d = 42.35 which becomes d = 121.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the number of dimes is 121.<BR>\n" );
document.write( "the number of nickels is 5 * the number of dimes is 121*5 = 605.<BR>\n" );
document.write( "121 * .1 = 12.1<BR>\n" );
document.write( ".05 * 605 = 30.25<BR>\n" );
document.write( "30.25 + 12.1 = 42.35<BR>\n" );
document.write( "your answer is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the key here is the number of nickels and dimes and the value of each.<BR>\n" );
document.write( "n = number of nickels and .05 * n = value of the number of nickels<BR>\n" );
document.write( "d = number of dimes and .1 * d = value of the number of dimes<BR>\n" );
document.write( ".05*n + .1*d = 42.35 is the value equation you have to work with.<BR>\n" );
document.write( "you can substitute 5d for n because the number of nickels = 5 times the number of dimes as stated.<BR>\n" );
document.write( "this does not change anything else in the value equation except that n has been replaced with 5d because the number of nickels is equal to the number of dimes.<BR>\n" );
document.write( "this allows you to reduce the number of unknowns in your equation from 2 to 1 which allows you to solve for the number of dimes which then allows you to solve for the number of nickels.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );