document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199078>Question 199078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have?\r<BR>\n" );
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document.write( "I have no idea where to start with this the best I can do is to subtract 6.05 from 9.85 but I don't know how to find the answer to this problem.  I do have to show my work but I am confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149534 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=149534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n=number of nickels and d=number of dimes\r<BR>\n" );
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document.write( "Since \"Joe has a collection of nickels and dimes worth $6.05\", this tells that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n%2B0.10d=6.05 ALIGN=MIDDLE  ALT=\"0.05n%2B0.10d=6.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiply EVERY term by 100 (to make every number whole) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=605 ALIGN=MIDDLE  ALT=\"5n%2B10d=605\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=605 ALIGN=MIDDLE  ALT=\"5n%2B10d=605\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, \"the number of dimes was doubled and the number of nickels was decreased by 10, the value would be $9.85\" means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05%28n-10%29%2B0.10%282d%29=9.85 ALIGN=MIDDLE  ALT=\"0.05%28n-10%29%2B0.10%282d%29=9.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Distribute to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05n-0.5%2B0.2d=9.85 ALIGN=MIDDLE  ALT=\"0.05n-0.5%2B0.2d=9.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiply EVERY term by 100 to make every number positive. So we now get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n-50%2B20d=985 ALIGN=MIDDLE  ALT=\"5n-50%2B20d=985\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Add 50 to both sides to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B20d=1035 ALIGN=MIDDLE  ALT=\"5n%2B20d=1035\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the second equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B20d=1035 ALIGN=MIDDLE  ALT=\"5n%2B20d=1035\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have the system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%285n%2B10d=605%2C5n%2B20d=1035%29 ALIGN=MIDDLE  ALT=\"system%285n%2B10d=605%2C5n%2B20d=1035%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=-1%285n%2B10d%29=-1%28605%29 ALIGN=MIDDLE  ALT=\"-1%285n%2B10d%29=-1%28605%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by -1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n-10d=-605 ALIGN=MIDDLE  ALT=\"-5n-10d=-605\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28-5n-10d=-605%2C5n%2B20d=1035%29 ALIGN=MIDDLE  ALT=\"system%28-5n-10d=-605%2C5n%2B20d=1035%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5n-10d%29%2B%285n%2B20d%29=%28-605%29%2B%281035%29 ALIGN=MIDDLE  ALT=\"%28-5n-10d%29%2B%285n%2B20d%29=%28-605%29%2B%281035%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=%28-5n%2B5n%29%2B%28-10d%2B20d%29=-605%2B1035 ALIGN=MIDDLE  ALT=\"%28-5n%2B5n%29%2B%28-10d%2B20d%29=-605%2B1035\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0n%2B10d=430 ALIGN=MIDDLE  ALT=\"0n%2B10d=430\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10d=430 ALIGN=MIDDLE  ALT=\"10d=430\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28430%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"d=%28430%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   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=d=43 ALIGN=MIDDLE  ALT=\"d=43\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n-10d=-605 ALIGN=MIDDLE  ALT=\"-5n-10d=-605\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go back to the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n-10%2843%29=-605 ALIGN=MIDDLE  ALT=\"-5n-10%2843%29=-605\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=43 ALIGN=MIDDLE  ALT=\"d=43\"   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=-5n-430=-605 ALIGN=MIDDLE  ALT=\"-5n-430=-605\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n=-605%2B430 ALIGN=MIDDLE  ALT=\"-5n=-605%2B430\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=430 ALIGN=MIDDLE  ALT=\"430\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5n=-175 ALIGN=MIDDLE  ALT=\"-5n=-175\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=%28-175%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"n=%28-175%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   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=n=35 ALIGN=MIDDLE  ALT=\"n=35\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=35 ALIGN=MIDDLE  ALT=\"n=35\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=43 ALIGN=MIDDLE  ALT=\"d=43\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that there are 35 nickels and 43 dimes </SPAN>\n" );
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