document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233614>Question 233614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost of producing an initial bicycle is £1200 and each successive bicycle there after cost £50 less than the last one. How many bicycles can be made for £10000?\r<BR>\n" );
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document.write( "I believe I know the formula, however because the Sn is 'less than' I cant seem to get to the answer!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172418 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=172418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost of producing an initial bicycle is £1200 and each successive bicycle there after cost £50 less than the last one. How many bicycles can be made for £10000? <BR>\n" );
document.write( "I believe I know the formula, however because the Sn is 'less than' I cant seem to get to the answer!!<BR>\n" );
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document.write( "Series: 1200 + 1150 + 1100 + ... <BR>\n" );
document.write( "S(n) < 10,000<BR>\n" );
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document.write( "a = 1200 and d = -50<BR>\n" );
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document.write( "Solve: <BR>\n" );
document.write( "S(n) = (n/2)(a(1) + a(n))<BR>\n" );
document.write( "10000 = (n/2)(1200 + a(n))<BR>\n" );
document.write( "20000=  (n)(1200 + 1200 +(n-1)(-50))<BR>\n" );
document.write( "20000 = (n)(2400 -50n+50)<BR>\n" );
document.write( "20000 = n(2450 - 50n)<BR>\n" );
document.write( "-50n^2 +2450n - 20000 = 0<BR>\n" );
document.write( "n^2 - 49n + 400 = 0<BR>\n" );
document.write( "n = 38.65 or n = 10.35<BR>\n" );
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document.write( "Now consider the inequality:<BR>\n" );
document.write( "20000 < n(2450n-50n)<BR>\n" );
document.write( "n^2 -49n + 400 < 0<BR>\n" );
document.write( "The parabola opens up so the <BR>\n" );
document.write( "solutions for the inequality are <BR>\n" );
document.write( "between the roots.<BR>\n" );
document.write( "10.35 < n < 38.65<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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