document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033082>Question 1033082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> there are pennies, nickels , dimes , and quarters in a piggy bank. if there are 14 coins in the bank and their value is $1.05\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647677 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=647677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Four unknown variables and two equations.  The easiest restriction is on how many quarters, being some natural number from 1 to 4.\r<BR>\n" );
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document.write( "p, n, d, q the count of each coin.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01p%2B0.05n%2B0.1d%2B0.25q=1.05 ALIGN=MIDDLE  ALT=\"0.01p%2B0.05n%2B0.1d%2B0.25q=1.05\"   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%2B10d%2B25q=105 ALIGN=MIDDLE  ALT=\"p%2B5n%2B10d%2B25q=105\"   DISABLED_style= \"max-width:90%; height:auto;\" > from account of the money value\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bn%2Bd%2Bq=14 ALIGN=MIDDLE  ALT=\"p%2Bn%2Bd%2Bq=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > the account of the coins\r<BR>\n" );
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document.write( "Solve each for p and equate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p=105-5n-10d-25q%2Cp=14-n-d-q%29 ALIGN=MIDDLE  ALT=\"system%28p=105-5n-10d-25q%2Cp=14-n-d-q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=105-5n-10d-25q=14-n-d-q ALIGN=MIDDLE  ALT=\"105-5n-10d-25q=14-n-d-q\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n-10d-25q%2Bn%2Bd%2Bq=14-105 ALIGN=MIDDLE  ALT=\"-5n-10d-25q%2Bn%2Bd%2Bq=14-105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4n-9d-24q=-91 ALIGN=MIDDLE  ALT=\"-4n-9d-24q=-91\"   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%284n%2B9d%2B24q=91%29 ALIGN=MIDDLE  ALT=\"highlight_green%284n%2B9d%2B24q=91%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "CASES FOR THE QUARTERS<BR>\n" );
document.write( "q=4<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%2B9d=-5 ALIGN=MIDDLE  ALT=\"4n%2B9d=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "q=3<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%2B9d=19 ALIGN=MIDDLE  ALT=\"4n%2B9d=19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "q=2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%2B9d=43 ALIGN=MIDDLE  ALT=\"4n%2B9d=43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "q=1<BR>\n" );
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document.write( "Which of these cases will work to give the right whole number values for n and d?\r<BR>\n" );
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document.write( "Look at a graph for case q=1.  Treat vertical axis as d, horizontal as n,<BR>\n" );
document.write( "looks bad!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C15%2C-1%2C15%2C-%284%2F9%29x%2B66%2F9%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C15%2C-1%2C15%2C-%284%2F9%29x%2B66%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph n and d for case q=2,<BR>\n" );
document.write( "guess is that still not good.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C-4x%2F9%2B43%2F9%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C-4x%2F9%2B43%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "See for case q=3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C10%2C-1%2C10%2C-4x%2F9%2B19%2F9%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C10%2C-1%2C10%2C-4x%2F9%2B19%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maybe....\r<BR>\n" );
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document.write( "A different way could be play with the simplest combination of coins to give $1.05 and split some coins to get a count of 14.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28q=4%2Cn=1%2Cc=5%29 ALIGN=MIDDLE  ALT=\"system%28q=4%2Cn=1%2Cc=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, c for count of coins but we must have c=14.  Splitting the nickel might not help much, at least not yet.\r<BR>\n" );
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document.write( "Split one quarter.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28q=3%2Cd=2%2Cn=2%2Cc=7%29 ALIGN=MIDDLE  ALT=\"system%28q=3%2Cd=2%2Cn=2%2Cc=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----still not enough coins c.\r<BR>\n" );
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document.write( "Split one more quarter.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28q=2%2Cd=4%2Cn=3%2Cc=9%29 ALIGN=MIDDLE  ALT=\"system%28q=2%2Cd=4%2Cn=3%2Cc=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >----we want to be able to get an even number of coins.\r<BR>\n" );
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document.write( "Maybe split one nickel from that.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28q=2%2Cd=4%2Cn=2%2Cp=5%2Cc=13%29 ALIGN=MIDDLE  ALT=\"system%28q=2%2Cd=4%2Cn=2%2Cp=5%2Cc=13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----we want ONE more coin, so maybe split one dime.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28Try+then+q=2%2Cd=3%2Cn=4%2Cp=5%2Cc=14%29 ALIGN=MIDDLE  ALT=\"system%28Try+then+q=2%2Cd=3%2Cn=4%2Cp=5%2Cc=14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----THIS must be the combination.<BR>\n" );
document.write( "2 quarters<BR>\n" );
document.write( "3 dimes<BR>\n" );
document.write( "4 nickels<BR>\n" );
document.write( "5 pennies<BR>\n" );
document.write( "--That is 14 coins. </SPAN>\n" );
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