document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184165>Question 1184165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jerome wanted to decorate a room by hanging rows of wooden beads across the <BR>\n" );
document.write( "windows. He strung 1/3 of the beads in 7 long pieces of string and 4/9 of the beads in<BR>\n" );
document.write( "16 short pieces of string. He kept the rest of the beads in a container. Each long piece<BR>\n" );
document.write( "of string had 15 more beads than each short piece of string.<BR>\n" );
document.write( "(a)   What fraction of the beads was kept in the container?<BR>\n" );
document.write( "(b)   How many beads did Jerome use to create his decoration? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821443 by </B><A HREF=/tutors/aboutme.mpl?userid=Octo-pie7><B>Octo-pie7(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Octo-pie7><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=Octo-pie7><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) fraction of beads which was kept in container = <BR>\n" );
document.write( "1 - (1/3 + 4/9) = 1 - ((3 + 4)/9)<BR>\n" );
document.write( "= 1 - 7/9<BR>\n" );
document.write( "= (9 - 7)/9<BR>\n" );
document.write( "= 2/9<BR>\n" );
document.write( "fraction of beads kept in container = 2/9<BR>\n" );
document.write( "(b) Let the total beads be x and y be the number of beads in short string<BR>\n" );
document.write( "it is given that 1/3 of the beads are used in 7 long pieces of string and each long piece string had 15 more beads than each short string.<BR>\n" );
document.write( "-> 1/(x) = 7(y + 15)<BR>\n" );
document.write( "-> x = 21(y+15) - (1)\r<BR>\n" );
document.write( "\n" );
document.write( "It is given that 4/9 of the beads are used in 16 short pieces of string.<BR>\n" );
document.write( "-> 4/9x = 16y<BR>\n" );
document.write( "-> x = 16 * 9/4y<BR>\n" );
document.write( "-> x = 36y -(1)<BR>\n" );
document.write( "from (1) and (2)<BR>\n" );
document.write( "36y = 21(y + 15)<BR>\n" );
document.write( "-> 36y = 21y + 315<BR>\n" );
document.write( "-> 36 - 21y = 315<BR>\n" );
document.write( "-> 15y = 315<BR>\n" );
document.write( "-> y = 315/15 = 21<BR>\n" );
document.write( "using this in (2) we have<BR>\n" );
document.write( "x + 36 * 21 = 756<BR>\n" );
document.write( "Total number of beads were 756 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );