document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68860>Question 68860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A collection of quarters and dimes is worth $6.75.  The number of dimes is 4 less than three times the number of quarters.  How many of each are there?\r<BR>\n" );
document.write( "\n" );
document.write( "I am confused as to how I would write this out, and solve it.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49003 by </B><A HREF=/tutors/aboutme.mpl?userid=rmromero><B>rmromero(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rmromero><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=49003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is asked in the problem?<BR>\n" );
document.write( "How many of dimes and quarters are there.<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "Collection of dimes and quarters is worth $6.75.<BR>\n" );
document.write( "The number of dimes is 4 less than 3 times the number of quarters.<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Representation:<BR>\n" );
document.write( "Let x = number of quarters.<BR>\n" );
document.write( "    y = number of quarters.<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Rewrite the given sentences to mathematical equation. <BR>\n" );
document.write( "The number of dimes is 4 less than 3 times the number of quarters.<BR>\n" );
document.write( "x = 3y - 4<BR>\n" );
document.write( "Collection of dimes and quarters is worth $6.75.<BR>\n" );
document.write( "0.10x + 0.25y = $6.75 --> 10x + 25y = 675. You can multiply 100 each term so that we will not deal with decimals.<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Solve the two equation using Substitution Method. <BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Here are the Steps using Substition method\r<BR>\n" );
document.write( "\n" );
document.write( "1. In either equation, solve for one variable in terms of the other.<BR>\n" );
document.write( "x = 3y - 4<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "2. Substitute for that variable in the other equation. Solve y.<BR>\n" );
document.write( "10x + 25y = 675<BR>\n" );
document.write( "10(3y - 4) + 25y = 675<BR>\n" );
document.write( "30y - 40 + 25y = 675<BR>\n" );
document.write( "55y = 715<BR>\n" );
document.write( "y = 13 ----> number of quarters<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "3. Substitute the result from step 2 in either equation. Solve for the other variable.<BR>\n" );
document.write( "x = 3y - 4 , y = 13<BR>\n" );
document.write( "x = 3(13) - 4<BR>\n" );
document.write( "x = 39 - 4<BR>\n" );
document.write( "x = 35 -----> number of dimes<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "4. Check the solution in both original equations.<BR>\n" );
document.write( "0.10x + 0.25y = $6.75 , x = 35, y = 13<BR>\n" );
document.write( "0.10(35) + 0.25(13) = $6.75 <BR>\n" );
document.write( "$3.50 + $3.25 = $6.75<BR>\n" );
document.write( "$6.75 = $6.75 --------------->> True\r<BR>\n" );
document.write( "\n" );
document.write( "<br> <BR>\n" );
document.write( "x = 3y - 4 , x = 35, y = 13<BR>\n" );
document.write( "35 = 3(13) - 4<BR>\n" );
document.write( "35 = 39 - 4<BR>\n" );
document.write( "35 = 35 ---------->> True\r<BR>\n" );
document.write( "\n" );
document.write( "<br> Therefore, the number of dimes are 35 and quarters 13.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );