document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61800>Question 61800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A library charges a fixed amount for the first day that a book is overdue and an additional charge for each day thereafter. Raoul paid $0.75 for one book that was 7 days overdue and $1.95 for a book that was 19 days overdue. Find the fixed charge and the charge for each additional day. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42566 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=42566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n = the number of days that a book is overdue. <BR>\n" );
document.write( "Let f = fixed amount for the first day a book is overdue.<BR>\n" );
document.write( "Let a = additional charge for each day after the first day.\r<BR>\n" );
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document.write( "Then, the fee for a book that's n days overdue is f+(n-1)*a.<BR>\n" );
document.write( "This is because of the fixed rate, f, plus a charge of a per additional day, but not for the first day. That's why it's (n-1) and not n.\r<BR>\n" );
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document.write( "Raoul paid 75 cents for a 7 day overdue book. So, f+(7-1)*a = 75, or f+6a = 75.<BR>\n" );
document.write( "Raoul also paid 195 cents for a book 19 days overdue. So, f+(19-1)*a = 195 or f+18a = 195.\r<BR>\n" );
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document.write( "So, we have two equations to solve together: f+6a=75 and f+18a=195.<BR>\n" );
document.write( "Subtract the first equation from the second and you get 12a=120 so a=10.<BR>\n" );
document.write( "Since f+6a = 75 and a=10 we know that f+60=75 so f=15.\r<BR>\n" );
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document.write( "So, the first day late fee is 15 cents and additional days cost 10 cents.\r<BR>\n" );
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document.write( "To verify:\r<BR>\n" );
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document.write( "The 7 day overdue book cost 15 cents for the first day and 10 cents for each of the other six days (60) so the total was 15+60 = 75 which is what the problem states.\r<BR>\n" );
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document.write( "The 19 day overdue book cost 15 cents for the first day and 10 cents for each of the other 18 days (180 cents) so the total was 15+180 = 195. </SPAN>\n" );
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