document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478795>Question 478795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this question!!<BR>\n" );
document.write( "Sam has some quarters, nickels, and dimes. He has 4 more <BR>\n" );
document.write( "quarters than dimes and 3 more dimes than nickels. If n<BR>\n" );
document.write( "represents the number of nickels he has, which of the<BR>\n" );
document.write( "following represents, in cents, the total value of all his<BR>\n" );
document.write( "coins?<BR>\n" );
document.write( "A. 40n + 205<BR>\n" );
document.write( "B. 40n + 130<BR>\n" );
document.write( "C. 40n + 7<BR>\n" );
document.write( "D. 7n + 130<BR>\n" );
document.write( "E. 3n + 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328052 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=328052\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i get 40n + 205<BR>\n" );
document.write( "we can test to see if this is accurate.<BR>\n" );
document.write( "first we'll solve.<BR>\n" );
document.write( "n = number of nickels.<BR>\n" );
document.write( "d = number of dimes<BR>\n" );
document.write( "q = number of quarters<BR>\n" );
document.write( "he has 4 more quarters than dimes.<BR>\n" );
document.write( "this leads to the equation:<BR>\n" );
document.write( "q = d + 4<BR>\n" );
document.write( "he has 3 more dimes than nickels<BR>\n" );
document.write( "this leads to the equation:<BR>\n" );
document.write( "d = n + 3<BR>\n" );
document.write( "since d = n + 3 and q = d + 4, this means that:<BR>\n" );
document.write( "q = (n+3)+4 which leads to:<BR>\n" );
document.write( "q = n+7<BR>\n" );
document.write( "so we have:<BR>\n" );
document.write( "d = n + 3<BR>\n" );
document.write( "q = n + 7<BR>\n" );
document.write( "now we need to get to the value equation.<BR>\n" );
document.write( "a quarter is worth 25 cents, so we multiply the number of quarters by 25 to get their value in cents.<BR>\n" );
document.write( "a dime is worth 10 cents, so we multiply the number of dimes by 10 to get their value in cents.<BR>\n" );
document.write( "a nickel is worth 5 cents, so we multiply the number of nickels by 5 to get their value in cents.<BR>\n" );
document.write( "the total value of our money is:<BR>\n" );
document.write( "25q + 10d + 5n<BR>\n" );
document.write( "since q is equal to n+7 and d is equal to n+3, we can replace q and d in this equation to get:<BR>\n" );
document.write( "25(n+7) + 10(n+3) + 5n<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "25n + 175 + 10n + 30 + 5n<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "40n + 205<BR>\n" );
document.write( "that's the value of our money.<BR>\n" );
document.write( "now let's see if this equation makes sense.<BR>\n" );
document.write( "suppose we have 100 nickels.<BR>\n" );
document.write( "the total value of our money should be:<BR>\n" );
document.write( "40*100 + 205 = 4205 cents<BR>\n" );
document.write( "we are saying that 25q + 10d + 5n = 4205<BR>\n" );
document.write( "n = 100<BR>\n" );
document.write( "d = n+3 = 103<BR>\n" );
document.write( "q = d+4 = 107<BR>\n" );
document.write( "25(107) + 10(103) + 5(100) should be equal to 4205 if everything is copacetic.<BR>\n" );
document.write( "multiplying these out gets us:<BR>\n" );
document.write( "2675 + 1030 + 500 = 4205<BR>\n" );
document.write( "the value of the money equals the same whether we used the initial equation or the final equation so we're good.<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "40n + 205 (selection A)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );