document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=834691>Question 834691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I think this goes here.\r<BR>\n" );
document.write( "\n" );
document.write( "I have this word problem and I can't seem to wrap my head around it.\r<BR>\n" );
document.write( "\n" );
document.write( "300 people attend an interview<BR>\n" );
document.write( "100 had mobile phones (x)<BR>\n" );
document.write( "70 had Passports (y)<BR>\n" );
document.write( "140 had drivers licenses (z)\r<BR>\n" );
document.write( "\n" );
document.write( "40 had x+y<BR>\n" );
document.write( "30 had y+z<BR>\n" );
document.write( "60 had x+z<BR>\n" );
document.write( "10 had x+y+z\r<BR>\n" );
document.write( "\n" );
document.write( "How many had none?\r<BR>\n" );
document.write( "\n" );
document.write( "any help with this would be awesome! Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503152 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=503152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A venn diagram really helps you visualize what is going on. So start off by drawing 3 overlapping circles inside a rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10 had x+y+z (aka 10 had all 3). Keep this in mind for the next parts. This value goes in the very center of the 3 overlapping circles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 had x+z. So this means that 60-10 = 50 had only x and z but not y. Notice how we took out the people who had all 3 to make sure of this. This number 50 goes in the region between X and Z (but NOT in any region where Y is overlapping).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Similarly, 30 had y+z, so 30-10 = 20 had only y and z but not x. The number 30 goes in the region between Y and Z (but NOT x). Also, 40 had x+y which means 40-10 = 30 had only x and y but not z. Write the number 40 in the region between X and Y (but not z)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now we must fill out the rest of the circular regions of the venn diagram. In the x circle for instance, all of the numbers must add to 100 (since there are 100 people who are in region x), so\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 50 + 10 + 30 = 100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 90 = 100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 100 - 90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The other values are found the same way\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y + 30 + 10 + 20 = 70\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y + 60 = 70\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 70 - 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z + 50 + 10 + 20 = 140\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z + 80 = 140\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = 140 - 80\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Finally, we add up all the values in the circular regions (but not outside the 3 circles) to get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10+30+10+50+10+20+60 = 190\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that there are 190 people who...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a) have just one thing x, y or z\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b) have 2 things (x+y, x+z, y+z)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "OR\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c) have all 3 things (x+y+z)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are 300 - 190 = <font color=\"red\">110 people</font> who have none of these 3 things.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here is what the venn diagram would look like:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://i150.photobucket.com/albums/s91/jim_thompson5910/untitled8_zpsd74be0f7.png\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );