document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285547>Question 285547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A purse contains a collection of quarters, dimes, nickels, and pennies. The average value of the coins in the purse is 17 cents. If a penny is removed from the purse, the average value of the coins becomes 18 cents. How many nickels are in the purse?\r<BR>\n" );
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document.write( "(A) 2 (B) 5 (C) 0 (D) 1 (E) 8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207001 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average value would be<BR>\n" );
document.write( "(total value)/(number of coins)<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of quarters<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of dimes<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of nickels<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of pennies<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825q+%2B+10d+%2B+5n+%2B+p%29%2F%28q+%2B+d+%2B+n+%2B+p%29+=+17 ALIGN=MIDDLE  ALT=\"%2825q+%2B+10d+%2B+5n+%2B+p%29%2F%28q+%2B+d+%2B+n+%2B+p%29+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in cents)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25q+%2B+10d+%2B+5n+%2B+p+=+17%2A%28q+%2B+d+%2B+n+%2B+p%29 ALIGN=MIDDLE  ALT=\"25q+%2B+10d+%2B+5n+%2B+p+=+17%2A%28q+%2B+d+%2B+n+%2B+p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825q+%2B+10d+%2B+5n+%2B+1%2A%28p+-+1%29%29%2F%28q+%2B+d+%2B+n+%2B+p+-+1%29+=+18 ALIGN=MIDDLE  ALT=\"%2825q+%2B+10d+%2B+5n+%2B+1%2A%28p+-+1%29%29%2F%28q+%2B+d+%2B+n+%2B+p+-+1%29+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25q+%2B+10d+%2B+5n+%2B+p+-+1+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29 ALIGN=MIDDLE  ALT=\"25q+%2B+10d+%2B+5n+%2B+p+-+1+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25q+%2B+10d+%2B+5n+%2B+p+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29+%2B+1 ALIGN=MIDDLE  ALT=\"25q+%2B+10d+%2B+5n+%2B+p+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing (1) and (2) I can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2A%28q+%2B+d+%2B+n+%2B+p%29+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29+%2B+1 ALIGN=MIDDLE  ALT=\"17%2A%28q+%2B+d+%2B+n+%2B+p%29+=+18%2A%28q+%2B+d+%2B+n+%2B+p+-+1%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2A%28q+%2B+d+%2B+n+%2B+p%29+=+18%2A%28q+%2B+d+%2B+n+%2B+p%29+-+17 ALIGN=MIDDLE  ALT=\"17%2A%28q+%2B+d+%2B+n+%2B+p%29+=+18%2A%28q+%2B+d+%2B+n+%2B+p%29+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2A%28q+%2B+d+%2B+n+%2B+p%29 ALIGN=MIDDLE  ALT=\"17%2A%28q+%2B+d+%2B+n+%2B+p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+q+%2B+d+%2B+n+%2B+p+-+17 ALIGN=MIDDLE  ALT=\"0+=+q+%2B+d+%2B+n+%2B+p+-+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+%2B+d+%2B+n+%2B+p+=+17 ALIGN=MIDDLE  ALT=\"q+%2B+d+%2B+n+%2B+p+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going back to (1),<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825q+%2B+10d+%2B+5n+%2B+p%29%2F%28q+%2B+d+%2B+n+%2B+p%29+=+17 ALIGN=MIDDLE  ALT=\"%2825q+%2B+10d+%2B+5n+%2B+p%29%2F%28q+%2B+d+%2B+n+%2B+p%29+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825q+%2B+10d+%2B+5n+%2B+p%29%2F17+=+17 ALIGN=MIDDLE  ALT=\"%2825q+%2B+10d+%2B+5n+%2B+p%29%2F17+=+17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25q+%2B+10d+%2B+5n+%2B+p+=+289 ALIGN=MIDDLE  ALT=\"25q+%2B+10d+%2B+5n+%2B+p+=+289\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in cents)<BR>\n" );
document.write( "There must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > coins, making <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=289 ALIGN=MIDDLE  ALT=\"289\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents <BR>\n" );
document.write( "I know there must be at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > pennies<BR>\n" );
document.write( "and there could be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" > pennies<BR>\n" );
document.write( "There can't be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarters, since that adds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents<BR>\n" );
document.write( "There can't be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarters either, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > dime and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > nickel make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=275+%2B+10+%2B+5+=+290 ALIGN=MIDDLE  ALT=\"275+%2B+10+%2B+5+=+290\"   DISABLED_style= \"max-width:90%; height:auto;\" > -too much<BR>\n" );
document.write( "Suppose there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarters, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > dime, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > nickel,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > pennies<BR>\n" );
document.write( "That makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=250+%2B+10+%2B+5+%2B+4+=+269 ALIGN=MIDDLE  ALT=\"250+%2B+10+%2B+5+%2B+4+=+269\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+%2B+1+%2B+1+%2B+4+=+16 ALIGN=MIDDLE  ALT=\"10+%2B+1+%2B+1+%2B+4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > coins<BR>\n" );
document.write( "and I can't make up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > more coin<BR>\n" );
document.write( "I'm guessing there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > quarters -you can figure out the rest\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );