document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181055>Question 181055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jar with pennies, nickels, and dimes contains a total of 55 coins worth $3.23. How many of each are there if the number of pennies is 10 less than the sum of nickels and dimes together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135905 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=135905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> YOU NEED TO RECHECK YOUR PROBLEM. UNLESS I MADE A MISTAKE, WE ARE COMING OUT WITH FRACTIONS OF COINS AND WE CAN'T HAVE FRACTIONS OF COINS.<BR>\n" );
document.write( "Let x=number of pennies<BR>\n" );
document.write( "y=number of nickels<BR>\n" );
document.write( "z=number of dimes<BR>\n" );
document.write( "Then:<BR>\n" );
document.write( "x+y+z=55-----------------eq1<BR>\n" );
document.write( "Lets deal in pennies<BR>\n" );
document.write( "x+5y+10z=323------------------eq2\r<BR>\n" );
document.write( "\n" );
document.write( "and<BR>\n" );
document.write( "x+10=y+z or<BR>\n" );
document.write( "x-y-z=-10 or<BR>\n" );
document.write( "x-(y+z)=-10----------------------eq3<BR>\n" );
document.write( "but from eq1, y+z=55-x.  Substitute this into eq3<BR>\n" );
document.write( "x-(55-x)=-10 or<BR>\n" );
document.write( "x-55+x=-10 add 55 to each side<BR>\n" );
document.write( "2x=45-----------------------------------------NO GOOD!!!!\r<BR>\n" );
document.write( "\n" );
document.write( "LET'S TRY ANOTHER APPROACH:\r<BR>\n" );
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document.write( "subtract eq1 from eq2 and we get:<BR>\n" );
document.write( "4y+9z=268-----------------------------------eq1a<BR>\n" );
document.write( "subtract eq3 from eq2 and we get:<BR>\n" );
document.write( "6y+11z=333------------------------------------eq2a\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply eq1a by 3:<BR>\n" );
document.write( "12y+27z=804----------------------eq1b<BR>\n" );
document.write( "Multiply eq2a by 2:<BR>\n" );
document.write( "12y+22z=666--------------------------eq2b<BR>\n" );
document.write( "subtract eq2b from eq1b:<BR>\n" );
document.write( "5z=138-------------------------------------------NO GOOD!!!!!\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps---ptaylor\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );