document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=997320>Question 997320</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble figuring my math problem out. The problem is \"Molly has $5.45 in coins. She has two more nickels than dimes. She has nine fewer quarters than dimes. How many of each coin does she have?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #615462 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=615462\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have to assume that Molly has no pennies, half-dollar coins, or dollar coins.<BR>\n" );
document.write( "The problem does not tell you that, but maybe it should.\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "IF YOU STUDIED SYSTEMS OF LINEAR EQUATIONS:<BR>\n" );
document.write( "You start by defining three variables:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of nickels Molly has,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of dimes Molly has, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q ALIGN=MIDDLE  ALT=\"Q\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of quarters Molly has.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05N ALIGN=MIDDLE  ALT=\"0.05N\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has as nickels.<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10D ALIGN=MIDDLE  ALT=\"0.10D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has as dimes.<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25Q ALIGN=MIDDLE  ALT=\"0.25Q\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has as quarters.<BR>\n" );
document.write( "The half assumed fact that Molly has $5.45 in coins\" between nickels dimes and quarters, with no pennies, half-dollars, or dollars, means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05N%2B0.1D%2B0.25Q=5.45 ALIGN=MIDDLE  ALT=\"0.05N%2B0.1D%2B0.25Q=5.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one of your equations.<BR>\n" );
document.write( "\"She has two more nickels than dimes\" translates as the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=D%2B2 ALIGN=MIDDLE  ALT=\"N=D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "\"She has nine fewer quarters than dimes\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q=D-9 ALIGN=MIDDLE  ALT=\"Q=D-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "With all 3 equations, you have the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%280.05N%2B0.1D%2B0.25Q=5.45%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%280.05N%2B0.1D%2B0.25Q=5.45%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You can have a simpler system, if you simplify equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05N%2B0.1D%2B0.25Q=5.45 ALIGN=MIDDLE  ALT=\"0.05N%2B0.1D%2B0.25Q=5.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > by<BR>\n" );
document.write( "dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05=1%2F20 ALIGN=MIDDLE  ALT=\"0.05=1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or<BR>\n" );
document.write( "multiplying both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > (same thing, really).<BR>\n" );
document.write( "then you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2B2D%2B5Q=109 ALIGN=MIDDLE  ALT=\"N%2B2D%2B5Q=109\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is simpler.<BR>\n" );
document.write( "The system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%280.05N%2B0.1D%2B0.25Q=5.45%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%280.05N%2B0.1D%2B0.25Q=5.45%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28N%2B2D%2B5Q=109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28N%2B2D%2B5Q=109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is easy to solve by substitution,<BR>\n" );
document.write( "substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2B2 ALIGN=MIDDLE  ALT=\"D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%7D%7D+%2C+and+%7B%7B%7BD-9 ALIGN=MIDDLE  ALT=\"N%7D%7D+%2C+and+%7B%7B%7BD-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q ALIGN=MIDDLE  ALT=\"Q\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the first equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28N%2B2D%2B5Q=109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28N%2B2D%2B5Q=109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%28D%2B2%29%2B2D%2B5%28D-9%29=109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28%28D%2B2%29%2B2D%2B5%28D-9%29=109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28D%2B2%2B2D%2B5D-45=109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28D%2B2%2B2D%2B5D-45=109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288D-43=109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%288D-43=109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288D=43%2B109%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%288D=43%2B109%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288D=152%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%288D=152%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28D=152%2F8%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28D=152%2F8%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28D=19%2CN=D%2B2%2CQ=D-9%29 ALIGN=MIDDLE  ALT=\"system%28D=19%2CN=D%2B2%2CQ=D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28D=19%2CN=19%2B2%2CQ=19-9%29 ALIGN=MIDDLE  ALT=\"system%28D=19%2CN=19%2B2%2CQ=19-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28D=19%2CN=21%2CQ=10%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28D=19%2CN=21%2CQ=10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "IF YOU HAVE NOT STUDIED SYSTEMS OF LINEAR EQUATIONS:<BR>\n" );
document.write( "You carefully choose one variable to define, so that you can calculate everything from that variable:<BR>\n" );
document.write( "<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 Molly has.<BR>\n" );
document.write( "\"She has two more nickels than dimes\" means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2B2 ALIGN=MIDDLE  ALT=\"D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of nickels Molly has, and<BR>\n" );
document.write( "\"She has nine fewer quarters than dimes\" means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D-9 ALIGN=MIDDLE  ALT=\"D-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of quarters Molly has.<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05%28D%2B2%29 ALIGN=MIDDLE  ALT=\"0.05%28D%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has as nickels,<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10D%7D%29%7D=+amount+of++money+that+Molly+has+as+dimes%2C%0D%0A%24%7B%7B%7B0.25%28D-9%29 ALIGN=MIDDLE  ALT=\"0.10D%7D%29%7D=+amount+of++money+that+Molly+has+as+dimes%2C%0D%0A%24%7B%7B%7B0.25%28D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has as quarters, and<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05%28D%2B2%29%2B0.10D%2B0.25%28D-9%29 ALIGN=MIDDLE  ALT=\"0.05%28D%2B2%29%2B0.10D%2B0.25%28D-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.45 ALIGN=MIDDLE  ALT=\"5.45\"   DISABLED_style= \"max-width:90%; height:auto;\" >= amount of  money that Molly has in coins.<BR>\n" );
document.write( "Then you solve the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05%28D%2B2%29%2B0.10D%2B0.25%28D-9%29=5.45 ALIGN=MIDDLE  ALT=\"0.05%28D%2B2%29%2B0.10D%2B0.25%28D-9%29=5.45\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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