document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848318>Question 848318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack has dimes, nickels, and quarters worth $10.00. If he has 50 coins in total, how many coins will Jack have of each? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #511057 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39625)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=511057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d count of dimes<BR>\n" );
document.write( "n count of nickels<BR>\n" );
document.write( "q count of quarters\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Bn%2Bq=50 ALIGN=MIDDLE  ALT=\"d%2Bn%2Bq=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10d%2B0.05n%2B0.25q=10 ALIGN=MIDDLE  ALT=\"0.10d%2B0.05n%2B0.25q=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Simplify the money count equation for whole number coefficients.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d%2B5n%2B25q=1000 ALIGN=MIDDLE  ALT=\"10d%2B5n%2B25q=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d%2Bn%2B5q=200 ALIGN=MIDDLE  ALT=\"2d%2Bn%2B5q=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >--------\r<BR>\n" );
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document.write( "SYSTEM:<BR>\n" );
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document.write( "2d+n+5q=200<BR>\n" );
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document.write( "d+n+q=50<BR>\n" );
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document.write( "That is two equations and three unknown variables.  Something must be initially assumed constant.  Try taking n as a constant, k=n.\r<BR>\n" );
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document.write( "SYSTEM with k=n:<BR>\n" );
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document.write( "2d+5q=200-k<BR>\n" );
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document.write( "d+q=50-k<BR>\n" );
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document.write( "Try elimination.  Multiply the second equation by 2 and subtract from the first equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d%2B5q-%282d%2B2q%29=200-k-%282%2A50-2k%29 ALIGN=MIDDLE  ALT=\"2d%2B5q-%282d%2B2q%29=200-k-%282%2A50-2k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3q=200-k-100%2B2k ALIGN=MIDDLE  ALT=\"3q=200-k-100%2B2k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283q=100%2Bk%29 ALIGN=MIDDLE  ALT=\"highlight_green%283q=100%2Bk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28q=%28k%2B100%29%2F3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28q=%28k%2B100%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Try elimination again for the other variable.  Multiply the second equation by 5 and ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2d%2B5q-%285d%2B5q%29=200-k-%285%2A50-5k%29 ALIGN=MIDDLE  ALT=\"2d%2B5q-%285d%2B5q%29=200-k-%285%2A50-5k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3d=200-k-250%2B5k ALIGN=MIDDLE  ALT=\"-3d=200-k-250%2B5k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3d=-50%2B4k ALIGN=MIDDLE  ALT=\"-3d=-50%2B4k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28d=%2850-4k%29%2F%283%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28d=%2850-4k%29%2F%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A choice must be found of some whole number for k so that d and q each are also whole numbers.  MAYBE k=2 worth a test.<BR>\n" );
document.write( "k_____________q____________d<BR>\n" );
document.write( "2____________34____________14----------Combination appears to work, since k+q+d=50.\r<BR>\n" );
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document.write( "ANSWER:  A good result then is 2 nickels, 14 dimes, 34 quarters.<BR>\n" );
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