document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244834>Question 244834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person has quarters, dimes, nickels,and pennies with a total value of $3.86.  The number of nickels is twice the number of quarters. The number of quarters is two less than the number of dimes. There are 40 coins in all. Write and solve an equation to find the number of each coin.  I have figured out that there are eight quarters, sixteen nickels, ten dimes, and six pennies.  I can not figure out how to write an equation for this problem. Can you help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178999 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=178999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let \r<BR>\n" );
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document.write( "p = # of pennies,<BR>\n" );
document.write( "n = # of nickels<BR>\n" );
document.write( "d = # of dimes<BR>\n" );
document.write( "q = # of quarters\r<BR>\n" );
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document.write( "Since \"There are 40 coins in all\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bn%2Bd%2Bq=40 ALIGN=MIDDLE  ALT=\"p%2Bn%2Bd%2Bq=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie add up the individual coin counts to get the total). This is your first equation.\r<BR>\n" );
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document.write( "Because \"The number of nickels is twice the number of quarters\", we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2q ALIGN=MIDDLE  ALT=\"n=2q\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since \"The number of quarters is two less than the number of dimes\", we also know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=d-2 ALIGN=MIDDLE  ALT=\"q=d-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, because \"A person has quarters, dimes, nickels,and pennies with a total value of $3.86\", we get the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01p%2B0.05n%2B0.10d%2B0.25q=3.86 ALIGN=MIDDLE  ALT=\"0.01p%2B0.05n%2B0.10d%2B0.25q=3.86\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember that a penny is $0.01, a nickel is $0.05, a dime is $0.10, and a quarter is $0.25. If you multiply those individual values by their counts (the defined variables) and add them all up, you'll get the total coin value $3.86\r<BR>\n" );
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document.write( "So the fourth and final equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01p%2B0.05n%2B0.10d%2B0.25q=3.86 ALIGN=MIDDLE  ALT=\"0.01p%2B0.05n%2B0.10d%2B0.25q=3.86\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "At the end of the translations, you get the four equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28p%2Bn%2Bd%2Bq=40%2Cn=2q%2Cq=d-2%2C0.01p%2B0.05n%2B0.10d%2B0.25q=3.86%29 ALIGN=MIDDLE  ALT=\"system%28p%2Bn%2Bd%2Bq=40%2Cn=2q%2Cq=d-2%2C0.01p%2B0.05n%2B0.10d%2B0.25q=3.86%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From here, all you need to do is solve the system. There are plenty of options available, but I recommend using a calculator to set up a matrix to solve this problem.\r<BR>\n" );
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