document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979964>Question 979964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Phineas has $1.15 worth of coin in his pocket.  He has three more dimes than quarters and two more dimes than nickels. How much does he have in each coin? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601191 by </B><A HREF=/tutors/aboutme.mpl?userid=RicaMath><B>RicaMath(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RicaMath><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=601191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem can be solved by writing a few algebraic equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's define the following variables:<BR>\n" );
document.write( "d = number of dimes<BR>\n" );
document.write( "n = number of nickels<BR>\n" );
document.write( "q = number of quarters\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The problem states that the sum of all of these coins is $1.15.  Translating this into an equation, you get 0.1d + 0.05n + 0.25q = 1.15  (multiply each variable by the monetary value of each coin)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's convert the rest of the statements into equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "He has three more dimes than quarters <BR>\n" );
document.write( "d = q + 3  (the number of dimes equals 3 more than the number of quarters)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "...and two more dimes than nickels.<BR>\n" );
document.write( "d = n + 2  (the number of dimes equals 2 more than the number of nickels)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, we solve for each variable by doing a series of substitutions.  We can equate the two equations above together to temporarily remove d, and then solve for one of the variables.  For this, I will solve for n.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "q + 3 = n + 2<BR>\n" );
document.write( "<b>n = q + 1</b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, I will plug in this value of n into the first equation and solve for d.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.1d + 0.05n + 0.25q = 1.15<BR>\n" );
document.write( "0.1d + 0.05(q + 1) + 0.25q = 1.15<BR>\n" );
document.write( "0.1d + 0.05q + 0.05 + 0.25q = 1.15<BR>\n" );
document.write( "0.1d + 0.3q = 1.1<BR>\n" );
document.write( "0.1d = 1.1 - 0.3q<BR>\n" );
document.write( "<b>d = 11 - 3q</b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I can then plug this into the equation d = q + 3 and solve for q.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "11 - 3q = q + 3<BR>\n" );
document.write( "-4q = -8<BR>\n" );
document.write( "<b>q = 2 </b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that I know q = 2, I can plug this into d = q + 3 to solve for d.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d = 2 + 3 <BR>\n" );
document.write( "<b>d = 5</b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Last step is to take d = 5 and solve for n. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d = n + 2<BR>\n" );
document.write( "5 = n + 2<BR>\n" );
document.write( "<b>n = 3</b>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To check the answer, we can plug these values into the original equation:\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "0.1d + 0.05n + 0.25q = 1.15<BR>\n" );
document.write( "0.1(5) + 0.05(3) + 0.25(2) = 1.15<BR>\n" );
document.write( "0.5 + 0.15 + 0.5 = 1.15<BR>\n" );
document.write( "1.15 = 1.15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The equation checks out!  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final answer: Phineas has 2 quarters, 5 dimes, and 3 nickels. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );