document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198744>Question 198744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word problem; Joe has a collection of nickles 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( "10x2 + 6.05x + 9.85 = 0<BR>\n" );
document.write( "using the  formula I am not sure what numbers go to a,b, or c? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149241 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=149241\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Whatever gave you the idea that you needed a quadratic equation for this problem?  Read the problem carefully.\r<BR>\n" );
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document.write( "Let <b><i>d</i></b> represent the number of dimes.  Let <b><i>n</i></b> represent the number of nickels.  It will be convenient to convert the amounts from dollars and cents to just cents, that is: $6.05 is 605 cents and $9.85 is 985 cents.\r<BR>\n" );
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document.write( "Dimes are worth 10 cents each, so the value of the dimes that he has right now is <b>10<i>d</i></b> cents.  His nickels, at 5 cents each, are worth <b>5<i>n</i></b> cents.  Add them together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d + 5n = 605\">\r<BR>\n" );
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document.write( "Likewise, if you double the amount of dimes, you have <b>2<i>d</i></b> dimes which are worth <b>20<i>d</i></b> cents.  10 fewer nickels is <b><i>n</i> - 10</b> which are worth <b>5(<i>n</i> - 10)</b> cents.  Add them together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d + 5(n - 10) = 985\">\r<BR>\n" );
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document.write( "which needs to be re-written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d + 5n = 1035\">\r<BR>\n" );
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document.write( "Now you have two equations in two variables.  Multiply the first one by -1 so that the coefficients on one of them become additive inverses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -10d - 5n = -605\">\r<BR>\n" );
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document.write( "Then add this new equation to the other one we developed:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20d - 10d + 5n - 5n = 1035 - 605\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d = 430\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d = 43\">\r<BR>\n" );
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document.write( "So he has 43 dimes.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "43 dimes is $4.30, leaving $6.05 - $4.30 = $1.75 in nickels.  $1.75 divided by .05 = 35, so 35 nickels.  Twice the dimes, 86, is worth $8.60, 10 less nickels is 25, 25 nickels is worth $1.25.  $8.60 plus $1.75 = $9.85.  Answer checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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