document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=500675>Question 500675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student buys 5-cent, 10-cent, and 15-cent stamps, with a total value of $6.70. If the number of 5-cent stamps is 2 more than the number of 10-cent stamps, while the number of 15-cent stamps is 5 more than one half the number of 10 cent stamps, how many stamps of each denomination did the student obtain?\r<BR>\n" );
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document.write( "This is as far as I got (chart form):\r<BR>\n" );
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document.write( "                         # of stamps    Denomination   Value<BR>\n" );
document.write( "5 cent                        n+2           .05         .5n+10<BR>\n" );
document.write( "10 cent                       n             .10         .10n<BR>\n" );
document.write( "15 cent                      (1/2n)+5       .15         .15(1/2n)+5\r<BR>\n" );
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document.write( "I am suppose to get the answer of:\r<BR>\n" );
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document.write( "28 5 cent stamps, 26 10 cent stamps, and 18 15 cent stamps.  I have tried this problem numerous ways and cannot get to the whole numbers listed above.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #338224 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=338224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "So far, you have it exactly right.\r<BR>\n" );
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document.write( "The next step is to add all of the values.  The value of the 10 cent stamps is, as you said, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large .10n\">, the value of the 5 cent stamps is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large .05(n\ +\ 2)\"> and the value of the 15 cent stamps is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large .15(0.5n\ +\ 5)\">\r<BR>\n" );
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document.write( "These three values add up to the total value of the stamps, namely $6.70.\r<BR>\n" );
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document.write( "Now, since I hate decimal fraction coefficients, I'm going to change everything from dollars and fractions of dollars to whole number of cents.  First,, $6.70 is nothing more than 670 cents, and the three values of the individual denominations become <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10n\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5(n\ +\ 2)\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 15\left(\frac{1}{2}n\ +\ 5\right)\">.  Now add it all up:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5(n\ +\ 2)\ +\ 15\left(\frac{1}{2}n\ +\ 5\right)\ =\ 670\">\r<BR>\n" );
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document.write( "First let's get rid of the parentheses:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5n\ +\ 10\ +\ \frac{15}{2}n\ +\ 75\ =\ 670\">\r<BR>\n" );
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document.write( "And then get the RHS constants over into the LHS by adding the opposites:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10n\ +\ 5n\ +\ \frac{15}{2}n\ =\ 585\">\r<BR>\n" );
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document.write( "But we still have that pesky fraction -- with a denominator of 2.  Multiply by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 20n\ +\ 10n\ +\ 15n\ =\ 1170\">\r<BR>\n" );
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document.write( "Collect the terms in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 45n\ =\ 1170\">\r<BR>\n" );
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document.write( "Can you get it from here, remembering that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> represents the number of 10-cent stamps?\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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