document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156349>Question 156349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stamp collection consist of 3, 8 and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is $2.47. Find the number of 8 cent stamps in the collection. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115154 by </B><A HREF=/tutors/aboutme.mpl?userid=kdr><B>kdr(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kdr><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=115154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let t = number of three cent stamps, e = number of eight cent stamps, and f = number of fifteen cent stamps.\r<BR>\n" );
document.write( "\n" );
document.write( "Since the number of 8 cent stamps is one less than triple the number of 3 cent stamps, we can write this equation:<BR>\n" );
document.write( "e = 3t - 1\r<BR>\n" );
document.write( "\n" );
document.write( "Since the number of 15 cent stamps is six less than the number of 8 cent stamps, we can write this equaation:<BR>\n" );
document.write( "f = e - 6\r<BR>\n" );
document.write( "\n" );
document.write( "Let's substitute 3t-1 for e:\r<BR>\n" );
document.write( "\n" );
document.write( "f = 3t-1-6<BR>\n" );
document.write( "f =3t-7\r<BR>\n" );
document.write( "\n" );
document.write( "We can write an equation showing the total value of the stamps like this:\r<BR>\n" );
document.write( "\n" );
document.write( ".03t + .08e + .15f = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( "Now, since we have e and f in terms of t, let's substitute those expressions in the total equation:\r<BR>\n" );
document.write( "\n" );
document.write( ".03t + .08(3t-1) + .15(3t-7) = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( "Expanding we get:\r<BR>\n" );
document.write( "\n" );
document.write( ".03t + .24t - .08 + .45t - 1.05 = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( "Combining like terms we now have:\r<BR>\n" );
document.write( "\n" );
document.write( "(.03 + .24 + .45)t - 1.13 = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( ".72t - 1.13 = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( "Adding 1.13 to both sides, we now have:<BR>\n" );
document.write( ".72t = 3.60\r<BR>\n" );
document.write( "\n" );
document.write( "Dividing both sides by .72, we get:<BR>\n" );
document.write( ".72t/.72 = 3.6/.72<BR>\n" );
document.write( "t = 5\r<BR>\n" );
document.write( "\n" );
document.write( "Putting t into the first equation we had, we get:<BR>\n" );
document.write( "e = 3(5) - 1, so e = 14<BR>\n" );
document.write( "and putting 14 for e in the second equations, we get:<BR>\n" );
document.write( "f = 14 - 6, so  f = 8\r<BR>\n" );
document.write( "\n" );
document.write( "Finally, we have 5 three cent stamps, 14 eight cent stamps, and 8 fifteen cent stamps.\r<BR>\n" );
document.write( "\n" );
document.write( "Checking the result:<BR>\n" );
document.write( "5(.03) + 14(.08) + 8(.15) = 2.47<BR>\n" );
document.write( ".15 + 1.12 + 1.20 = 2.47<BR>\n" );
document.write( "2.47 = 2.47\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );