document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=757145>Question 757145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of college students, it was found that: <BR>\n" );
document.write( "356 owned an iPod <BR>\n" );
document.write( "293 owned a laptop <BR>\n" );
document.write( "285 owned a gaming system <BR>\n" );
document.write( "193 owned an iPod and laptop <BR>\n" );
document.write( "200 owned an iPod and gaming system <BR>\n" );
document.write( "139 owned a laptop and a gaming system <BR>\n" );
document.write( "68 owned an iPod, laptop and gaming system <BR>\n" );
document.write( "26 owned none of these devices <BR>\n" );
document.write( "Of the college students surveyed, how many owned a) exactly two of these devices b) at least one of these devises <BR>\n" );
document.write( "I am not sure if I am supposed to figure out how many students were surveyed to be able to solve this or what.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #460657 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=460657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It looks like all of the students were surveyed. Otherwise,<BR>\n" );
document.write( "you couldn't solve it. <BR>\n" );
document.write( "Draw three interlocking rings ( Venn diagram ) so that<BR>\n" );
document.write( "there is an area in the center which is common to<BR>\n" );
document.write( "all three rings.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "It's helpful to notice there are 8 categories listed and the<BR>\n" );
document.write( "Venn diagram divides into 7 areas. Everything outside<BR>\n" );
document.write( "the 3 rings is the last category: <BR>\n" );
document.write( "\" 26 owned none of the devices\"<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "The area in the center is:<BR>\n" );
document.write( "\"68 owned an iPod, laptop and gaming system\"<BR>\n" );
document.write( "Now there are 6 categories left<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "\"193 owned an iPod and laptop\"<BR>\n" );
document.write( "If you subtract 68, you get 125, which is the area<BR>\n" );
document.write( "( ipod + laptop ), but not ( ipod + laptop + gaming system )<BR>\n" );
document.write( "---------------------------------------------------<BR>\n" );
document.write( "\"200 owned an iPod and gaming system\"<BR>\n" );
document.write( "If you subtract 68, you get 132, which is the area<BR>\n" );
document.write( "( ipod + gaming system ), but not ( ipod + laptop + gaming system )<BR>\n" );
document.write( "----------------------------------------------------------<BR>\n" );
document.write( "\"139 owned a laptop and a gaming system\"<BR>\n" );
document.write( "If you subtract 68, you get 71, which is the area<BR>\n" );
document.write( "( laptop + gaming system ), but not ( ipod + laptop + gaming system )<BR>\n" );
document.write( "------------------------------------------------------------<BR>\n" );
document.write( "Now there are 3 categories left<BR>\n" );
document.write( "\"356 owned an iPod\"<BR>\n" );
document.write( "Now subtract ( 125 + 68 + 132 = 325 )<BR>\n" );
document.write( "356 minus 325 = 31<BR>\n" );
document.write( "These 31 own an ipod and nothing else<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "\"293 owned a laptop\"<BR>\n" );
document.write( "subtract { 71 + 68 + 125 = 264 )<BR>\n" );
document.write( "293 minus 264 = 29<BR>\n" );
document.write( "29 own a laptop and nothing else<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "\"285 owned a gaming system\"<BR>\n" );
document.write( "subtract ( 132 + 68 + 71 = 271 )<BR>\n" );
document.write( "285 minus 271 = 14<BR>\n" );
document.write( "14 own a laptop and nothing else<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "The number that owned exactly 2 of the devices is<BR>\n" );
document.write( "( 125 + 132 + 71 = 328 )<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "The number that owned at least 1 of the devices is<BR>\n" );
document.write( "The sum of all the areas:<BR>\n" );
document.write( "( 14 + 29 + 31 + 71 + 125 + 132 + 68 = 470 )<BR>\n" );
document.write( "Hope I got it\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );