document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=791824>Question 791824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jar has 50 coins: all pennies, nickles, and dimes, with a total value of $3.50. There are twice as many nickles as as pennies. How many are there of each coin?<BR>\n" );
document.write( "p=pennies           .01       .01p<BR>\n" );
document.write( "2p=nickles          .05       .05(2p)<BR>\n" );
document.write( "d=dimes             .10       .10(50-3p)=5-.30p<BR>\n" );
document.write( "         <BR>\n" );
document.write( "p+2p+d=50<BR>\n" );
document.write( "d=50-3p\r<BR>\n" );
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document.write( ".01p+.05(2p)+5-.3p=3.5<BR>\n" );
document.write( ".01p+.1p+5-.3p=3.5<BR>\n" );
document.write( "-.19p+5=3.5<BR>\n" );
document.write( "5-3.5=.19p<BR>\n" );
document.write( "1.5=.19p<BR>\n" );
document.write( "email is its.me.pinkey3@gmail.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479737 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=479737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> VARIABLES<BR>\n" );
document.write( "p = count pennies<BR>\n" );
document.write( "n = count nickels<BR>\n" );
document.write( "d = count dimes\r<BR>\n" );
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document.write( "TRANSLATE THE WORDED DESCRIPTIONS<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bn%2Bd=50 ALIGN=MIDDLE  ALT=\"p%2Bn%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01p%2B0.05n%2B0.10d=3.50 ALIGN=MIDDLE  ALT=\"0.01p%2B0.05n%2B0.10d=3.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Fp=2%2F1 ALIGN=MIDDLE  ALT=\"n%2Fp=2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (Twice as many nickels as pennies; ratio of nickels to pennies is 2:1).\r<BR>\n" );
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document.write( "MANAGE EQUATIONS TO MAKE SYSTEM EASIER TO SOLVE<BR>\n" );
document.write( "Clear the fractional nature of the money sum, multiplying both sides by 100, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5n%2B10d=350 ALIGN=MIDDLE  ALT=\"p%2B5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Multiply the ratio equation left&right by p, giving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2p ALIGN=MIDDLE  ALT=\"n=2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "ALGEBRAIC SOLUTION STEPS\r<BR>\n" );
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document.write( "The system is now this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5n%2B10d=350 ALIGN=MIDDLE  ALT=\"p%2B5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Bn%2Bd=50 ALIGN=MIDDLE  ALT=\"p%2Bn%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2p ALIGN=MIDDLE  ALT=\"n=2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Solution steps can use the less advanced method of substitution, starting with n.  Replace n in the first two equations with n=2p.  This gives two equations in two unknowns:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B5%2A2p%2B10d=350 ALIGN=MIDDLE  ALT=\"p%2B5%2A2p%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B2p%2Bd=50 ALIGN=MIDDLE  ALT=\"p%2B2p%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11p%2B10d=350 ALIGN=MIDDLE  ALT=\"11p%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3p%2Bd=50 ALIGN=MIDDLE  ALT=\"3p%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Various ways to go, but try solving the count equation for d, and substitute this into the money sum equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=50-3p ALIGN=MIDDLE  ALT=\"d=50-3p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, put into... 11p+10*(50-3p)=350<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11p%2B500-30p=350 ALIGN=MIDDLE  ALT=\"11p%2B500-30p=350\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-19p=350-500 ALIGN=MIDDLE  ALT=\"-19p=350-500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150=19p ALIGN=MIDDLE  ALT=\"150=19p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=7.89%29 ALIGN=MIDDLE  ALT=\"highlight%28p=7.89%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  MISTAKE?  (No.  See \"Second Thought\")\r<BR>\n" );
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document.write( "(some commentary removed)\r<BR>\n" );
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document.write( "SECOND THOUGHT:  My answer is like your answer.  The mistake is not in our work, but in the problem description.  \r<BR>\n" );
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document.write( "CORRECTION TO QUESTION:  Amount of money should have been $3.10; with this, problem was solved by original poster. </SPAN>\n" );
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