document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=234633>Question 234633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man has 35 coins consisting of dimes and quarters.  The total value is $5.15.  How many of each coin does he have?  I know that there are 24 dimes and 11 quarters (working it backwards) but I can't figure out what the equation should be to solve for this problem.  Can ANYONE please help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172994 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=172994\">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( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> represent the number of dimes.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\"> represent the number of quarters.  Each dime is worth 10 cents, so the value of the dimes, in cents is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10d\">.  Likewise, the value of the quarters is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 25q\">.  And the total value of all the coins, in cents, is 515.\r<BR>\n" );
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document.write( "Now we can write an equation that describes the number of coins:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ +\ q\ =\ 35\">\r<BR>\n" );
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document.write( "And another equation that describes the value of the coins:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 25q\ =\ 515\">\r<BR>\n" );
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document.write( "Giving you a system of two equations in two variables.  Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\">.  Since you have unity coefficients on the first equation, I would use the substitution method to solve this system.\r<BR>\n" );
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document.write( "Which leads me to the description of a shortcut method for solving coin and different value ticket problems.  Instead of defining a second variable as above, i.e. \"Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\"> represent the number of quarters\" you can realize up front that there are 35 coins, so if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\"> represents the number of dimes, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 35\ -\ d\"> must represent the number of quarters.  Then you can just write the single equation for the value thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d\ +\ 25(35\ -\ d)\ =\ 515\">\r<BR>\n" );
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document.write( "Which is exactly the same place you would be if you solved the first equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\"> and then substituted into the second equation.\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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