document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947343>Question 947343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 15 coins. Each coin is a penny,<BR>\n" );
document.write( "nickel, dime or quarter. The total value of these<BR>\n" );
document.write( "coins is $2.16. There is at least one coin of<BR>\n" );
document.write( "each denomination, and the number of pennies,<BR>\n" );
document.write( "nickels, dimes and quarters are all distinct. If<BR>\n" );
document.write( "there are 5 dimes, how many nickels are in the bag? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578004 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=578004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE BELOW, IMPROVEMENT/ALTERNATIVE\r<BR>\n" );
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document.write( "p, n, d, q;<BR>\n" );
document.write( "p+n+d+q=15.<BR>\n" );
document.write( "0.01p+0.05n+0.1d+0.25q=2.16.<BR>\n" );
document.write( "d=5.\r<BR>\n" );
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document.write( "Simplify the money count.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5n%2B10d%2B25q=216 ALIGN=MIDDLE  ALT=\"p%2B5n%2B10d%2B25q=216\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and substitute for d;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5n%2B10%2A5%2B25q=216 ALIGN=MIDDLE  ALT=\"p%2B5n%2B10%2A5%2B25q=216\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5n%2B25q=166 ALIGN=MIDDLE  ALT=\"p%2B5n%2B25q=166\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You have a system,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2B5n%2B25q=166%2Cp%2Bn%2B5%2Bq=15%29 ALIGN=MIDDLE  ALT=\"system%28p%2B5n%2B25q=166%2Cp%2Bn%2B5%2Bq=15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2B5n%2B25q=166%2Cp%2Bn%2Bq=10%29 ALIGN=MIDDLE  ALT=\"system%28p%2B5n%2B25q=166%2Cp%2Bn%2Bq=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can assume any one of p, or n, or q is constant, and then solve for the other two variables in terms of the chosen constant.  This is because you are assuming a two-variable, linear system.\r<BR>\n" );
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document.write( "As a guess, the number of quarters is probably not too large compared to the 15 count of coins.  Assign k=q.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2B5n=166-25k%2Cp%2Bn=10-k%29 ALIGN=MIDDLE  ALT=\"system%28p%2B5n=166-25k%2Cp%2Bn=10-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "E1-E2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n=%28166-25k%29-%2810-k%29 ALIGN=MIDDLE  ALT=\"4n=%28166-25k%29-%2810-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n=166-10-25k%2Bk ALIGN=MIDDLE  ALT=\"4n=166-10-25k%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n=156-24k ALIGN=MIDDLE  ALT=\"4n=156-24k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=39-6k ALIGN=MIDDLE  ALT=\"n=39-6k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Try to find p based on this formula for n.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bn=10-k ALIGN=MIDDLE  ALT=\"p%2Bn=10-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10-k-n ALIGN=MIDDLE  ALT=\"p=10-k-n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10-k-%2839-6k%29 ALIGN=MIDDLE  ALT=\"p=10-k-%2839-6k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10-39-k%2B6k ALIGN=MIDDLE  ALT=\"p=10-39-k%2B6k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-29%2B7k ALIGN=MIDDLE  ALT=\"p=-29%2B7k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "What will make sense for k?  In summary, we have a formula for p and a formula for n:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28n=39-6k%2Cp=7k-29%29 ALIGN=MIDDLE  ALT=\"system%28n=39-6k%2Cp=7k-29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "We must have natural numbers for each of n, p, k.  None of them be equal.  None of them over 13.\r<BR>\n" );
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document.write( "Choose and find.\r<BR>\n" );
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document.write( "k__________n________p<BR>\n" );
document.write( "1__________33_______-22<BR>\n" );
document.write( "2__________27_______-15<BR>\n" );
document.write( "3__________21_______-8<BR>\n" );
document.write( "4__________15_______-1<BR>\n" );
document.write( "5__________9________6,  still not good because need some nickels, 9+6=15.<BR>\n" );
document.write( "6__________3________13<BR>\n" );
document.write( "7__________-3<BR>\n" );
document.write( "FAILED TO RESOLVE THE PROBLEM...........................\r<BR>\n" );
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document.write( "IMPROVEMENT/ALTERNATIVE:<BR>\n" );
document.write( "Re-examining the description,  the two key equations are  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2B5n%2B25q=166%2Cp%2Bn%2Bq=10%29 ALIGN=MIDDLE  ALT=\"system%28p%2B5n%2B25q=166%2Cp%2Bn%2Bq=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which are based on the given assignment that d=5.\r<BR>\n" );
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document.write( "Subtracting the coin count equation from the money count equation (both being in their just stated simplified form), we have <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%2B24q=156 ALIGN=MIDDLE  ALT=\"4n%2B24q=156\"   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%28n%2B6q=39%29 ALIGN=MIDDLE  ALT=\"highlight_green%28n%2B6q=39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and p has been eliminated.\r<BR>\n" );
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document.write( "Using this simple equation relating n and q, try choosing different natural number values for q and find resulting n, and look for results which makes sense.\r<BR>\n" );
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document.write( "pick q____________find n<BR>\n" );
document.write( "1_________________33<BR>\n" );
document.write( "2_________________27<BR>\n" );
document.write( "3_________________21<BR>\n" );
document.write( "4_________________15<BR>\n" );
document.write( "5_________________9<BR>\n" );
document.write( "6_________________3--------THERE!!!  Their sum is only 9, allowing the....five dimes.\r<BR>\n" );
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document.write( "ANSWER RESULT<BR>\n" );
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document.write( "Combination appears to be:<BR>\n" );
document.write( "p=?<BR>\n" );
document.write( "n=3<BR>\n" );
document.write( "d=5<BR>\n" );
document.write( "q=6<BR>\n" );
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document.write( "p=15-3-5-6=1, because total coins must be 15<BR>\n" );
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document.write( "Notice all counts are unequal.<BR>\n" );
document.write( "One penny, three nickels, five dimes, six quarters.<BR>\n" );
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document.write( " </SPAN>\n" );
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