document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121934>Question 121934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve and show the equations used for the solution\r<BR>\n" );
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document.write( "Jill has $3.50 in nickels and dimes.  If she has 50 coins, how many of each type of coin does she have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89502 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have two relationships in a coin problem.  One relates the number of coins and the other concerns the value of the coins.\r<BR>\n" );
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document.write( "Let n be the number of nickels, and d be the number of dimes.  So we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Bd=50 ALIGN=MIDDLE  ALT=\"n%2Bd=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since nickels are worth 5 cents each, the value of the nickels in this problem is 5n cents.  Similarly, the value of the dimes is 10d cents.  Just to keep everything conveniently in terms of integers, let's convert $3.50 to 350 cents.  Now we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%2B10d=350 ALIGN=MIDDLE  ALT=\"5n%2B10d=350\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the first equation for n:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=50-d ALIGN=MIDDLE  ALT=\"n=50-d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and substitute this expression for n into the second equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%285%2Ared%28n%29%2B10d=350%2C5%2Ared%28%2850-d%29%29%2B10d=350%29 ALIGN=MIDDLE  ALT=\"cartoon%285%2Ared%28n%29%2B10d=350%2C5%2Ared%28%2850-d%29%29%2B10d=350%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now distribute the 5 and collect terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%28red%285%2A%2850-d%29%29%2B10d=350%2Cred%28250-5d%29%2B10d=350%29 ALIGN=MIDDLE  ALT=\"cartoon%28red%285%2A%2850-d%29%29%2B10d=350%2Cred%28250-5d%29%2B10d=350%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%28250+-red%285d%2B10d%29=350%2C250%2Bred%285d%29=350%29 ALIGN=MIDDLE  ALT=\"cartoon%28250+-red%285d%2B10d%29=350%2C250%2Bred%285d%29=350%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%28red%28250%29%2B5d=red%28350%29%2C5d=red%28350-250%29%2C5d=red%28100%29%29 ALIGN=MIDDLE  ALT=\"cartoon%28red%28250%29%2B5d=red%28350%29%2C5d=red%28350-250%29%2C5d=red%28100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cartoon%285d=red%28100%29%2Cd=red%2820%29%29 ALIGN=MIDDLE  ALT=\"cartoon%285d=red%28100%29%2Cd=red%2820%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So there are 20 dimes, and there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50-20=30 ALIGN=MIDDLE  ALT=\"50-20=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > nickels.\r<BR>\n" );
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document.write( "Check: 30 nickels are worth $1.50, 20 dimes are worth $2.00.  $1.50 plus $2.00 are $3.50.  Answer checks. </SPAN>\n" );
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