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" );
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document.write( "(a) The fraction left in the container is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-%281%2F3%29-%284%2F9%29=1-3%2F9-4%2F9=1-7%2F9=2%2F9 ALIGN=MIDDLE  ALT=\"1-%281%2F3%29-%284%2F9%29=1-3%2F9-4%2F9=1-7%2F9=2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "1/3 of the beads were used in 7 long strings, so each long string had (1/3)/7 = 1/21 of the total number of beads.<BR>\n" );
document.write( "4/9 of the beads were used in 16 short strings, so each short string had (4/9)/16 = 1/36 of the beads.<BR>\n" );
document.write( "The number of beads in each long string was 15 more than the number in each short string:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F21%29x=%281%2F36%29x%2B15 ALIGN=MIDDLE  ALT=\"%281%2F21%29x=%281%2F36%29x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F21%29x-%281%2F36%29x=15 ALIGN=MIDDLE  ALT=\"%281%2F21%29x-%281%2F36%29x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(multiply by the LCM of 36 and 21, which is 21*12=252)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-7x=15%2A252 ALIGN=MIDDLE  ALT=\"12x-7x=15%2A252\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=15%2A252 ALIGN=MIDDLE  ALT=\"5x=15%2A252\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2A252=756 ALIGN=MIDDLE  ALT=\"x=3%2A252=756\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The total number of beads was 756<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "1/3 of 756 is 252; 7 strings of 252/7=36 beads each<BR>\n" );
document.write( "4/9 of 756 is 336; 16 strings of 336/16=21 beads each<BR>\n" );
document.write( "36-21=15<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );