document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=648794>Question 648794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> liviana has $ 2.20 in coins in  her change purse. if there is a total of 15 coins how many quarters,dimes,nickles,and pennies does she have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #406825 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=406825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 4 unknowns but only 2 possible<BR>\n" );
document.write( "equations, so this can't be solved directly,<BR>\n" );
document.write( "but it still can be figured out.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+ ALIGN=MIDDLE  ALT=\"+p+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of pennies<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of nickels<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of dimes<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+q+ ALIGN=MIDDLE  ALT=\"+q+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of quarters<BR>\n" );
document.write( "The equations are:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p+%2B+n+%2B+d+%2B+q+=+15+ ALIGN=MIDDLE  ALT=\"+p+%2B+n+%2B+d+%2B+q+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Ap+%2B+5n+%2B+10d+%2B+25q+=+220+ ALIGN=MIDDLE  ALT=\"+1%2Ap+%2B+5n+%2B+10d+%2B+25q+=+220+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( in cents )<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "The logic steps are:<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "There doesn't have to be any pennies,<BR>\n" );
document.write( "although there might be, but they will be in<BR>\n" );
document.write( "multiples of 5 or 10<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "I know there must be less than 9 quarters, since<BR>\n" );
document.write( "9 x 25 = 225, which is too much<BR>\n" );
document.write( "(c)<BR>\n" );
document.write( "I know there must be more than 2 quarters since<BR>\n" );
document.write( "2 x 25 = 50, that leaves 13 coins to make $1.70<BR>\n" );
document.write( "and even if I have 13 dimes, that is only $1.30<BR>\n" );
document.write( "(d)<BR>\n" );
document.write( "Likewise, there must be more that 3 quarters<BR>\n" );
document.write( "3 x 25 = 75 and 220 - 75 = 145, and<BR>\n" );
document.write( "12 x10 = 120 which doesn't make it<BR>\n" );
document.write( "(e)<BR>\n" );
document.write( "Also, there must be more than 4 quarters <BR>\n" );
document.write( "4 x 25 = 100 and 220 - 100 = 120<BR>\n" );
document.write( "There are 11 coins left to make $1.20<BR>\n" );
document.write( "and 11 x 10 = 110, too small<BR>\n" );
document.write( "(f)<BR>\n" );
document.write( "It is possible with 5 quarters since<BR>\n" );
document.write( "5 x 25 = 125 and 220 - 125 = 95<BR>\n" );
document.write( "and 10 x 10 = 100, so it's possible<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "5q = 125 which is 5 coins leaving 10<BR>\n" );
document.write( "220 - 125 = 95<BR>\n" );
document.write( "9d = 90 leaving 1 coin<BR>\n" );
document.write( "1 x 5 = 5<BR>\n" );
document.write( "So, the answer is<BR>\n" );
document.write( "5q<BR>\n" );
document.write( "9d<BR>\n" );
document.write( "1n<BR>\n" );
document.write( "But if I have to use pennies it doesn't work<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "I'll try<BR>\n" );
document.write( "6q<BR>\n" );
document.write( "5d<BR>\n" );
document.write( "4n<BR>\n" );
document.write( "This works, but still no pennies<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "I'll try<BR>\n" );
document.write( "7q<BR>\n" );
document.write( "1d<BR>\n" );
document.write( "This leaves 7 coins to make 35 cents<BR>\n" );
document.write( "and no room for pennies<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "8q<BR>\n" );
document.write( "1d<BR>\n" );
document.write( "Leaves 6 coins to make 10 cents<BR>\n" );
document.write( "that's <BR>\n" );
document.write( "1n<BR>\n" );
document.write( "5p<BR>\n" );
document.write( "That's it<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "8 quarters, 1 dime, 1 nickel, and 5 pennies<BR>\n" );
document.write( "are 15 coins that make $2.20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );