document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=562230>Question 562230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ted knows about a marble machine that doubles the number of marbles you put in and adds 24 marbles. One day he put in a certain number  and got back a new number. He put the new number in the machine and got back 360 marbles. How many marbles did he put in the machine in the first place<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364503 by </B><A HREF=/tutors/aboutme.mpl?userid=issacodegard><B>issacodegard(60)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=issacodegard><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=issacodegard><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, let's denote the effect of the marble machine by the function,\r<BR>\n" );
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document.write( "f(n)=2n+24\r<BR>\n" );
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document.write( "Where we input n marbles and output 2n+24 marbles.\r<BR>\n" );
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document.write( "One day x marbles were input and thus f(x) marbles were output.  Then f(x) was input and thus output was f(f(x)) marbles, but as written in the problem was 360 marbles.\r<BR>\n" );
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document.write( "So we solve f(f(x))=360 for x\r<BR>\n" );
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document.write( "Therefore, we have\r<BR>\n" );
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document.write( "f(f(x))=f(2x+24)=2(2x+24)+24=4x+72=360\r<BR>\n" );
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document.write( "So, x=72, which was the original number of marbles input. </SPAN>\n" );
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