document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167409>Question 1167409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey carried out recently to find the number of applicants that applied for jobs into 3 newspaper establishment, revealed that 70 applied to daily times, 65 applied to Daily graphics and 85 applied to daily punch. 40 applied to daily times only, 20 applied to daily graphics only while 45 applied to daily punch only. If 15 applied to all three newspaper establishment, find:The number that applied to both daily times and daily graphics </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792002 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i got the answer, but it wasn't easy and i don't believe it lent itself to any specific formula very well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is what i got:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                            daily times         daily graphic      daily punch\r\n" );
document.write( "\r\n" );
document.write( "total                           70                    65                85\r\n" );
document.write( "1 only                          40                    20                45\r\n" );
document.write( "all 3                           15                    15                15\r\n" );
document.write( "1 only + all 3                  55                    35                60\r\n" );
document.write( "total - (1 only + all 3)        15                    30                25\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total - (1 only + all 3) means that each one of those is split between only 1 other, forming 2 only.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so the row with the title of total - (1 only + all 3) can be renamed to 2 only.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the table then looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                            daily times         daily graphic      daily punch\r\n" );
document.write( "\r\n" );
document.write( "total                           70                    65                85\r\n" );
document.write( "1 only                          40                    20                45\r\n" );
document.write( "all 3                           15                    15                15\r\n" );
document.write( "1 only + all 3                  55                    35                60\r\n" );
document.write( "2 only                          15                    30                25\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that 2 only row needs to be split into pairs rather than having entries in all 3 columns.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i had to play around with it until i got what looked like it should be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the end result was:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                            daily times         daily graphic      daily punch\r\n" );
document.write( "\r\n" );
document.write( "total                           70                    65                85\r\n" );
document.write( "1 only                          40                    20                45\r\n" );
document.write( "all 3                           15                    15                15\r\n" );
document.write( "1 only + all 3                  55                    35                60\r\n" );
document.write( "---------------------------------------------------------------------------\r\n" );
document.write( "daily times daily graphic       10                    10\r\n" );
document.write( "daily times daily punch          5                                       5\r\n" );
document.write( "daily graphic daily punch                             20                20\r\n" );
document.write( "---------------------------------------------------------------------------\r\n" );
document.write( "2 only                          15                    30                25\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the part between the dashed lines is the breakdown of the 2 only row.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your total is the data in the 1 only row and the 3 only row and the 2 only row.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                            daily times         daily graphic      daily punch\r\n" );
document.write( "\r\n" );
document.write( "1 only                          40                    20                45\r\n" );
document.write( "all 3                           15                    15                15\r\n" );
document.write( "2 only                          15                    30                25\r\n" );
document.write( "total                           70                    65                85\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you break the 2 only row down, then you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                            daily times         daily graphic      daily punch\r\n" );
document.write( "\r\n" );
document.write( "1 only                          40                    20                45\r\n" );
document.write( "all 3                           15                    15                15\r\n" );
document.write( "daily times daily graphic       10                    10\r\n" );
document.write( "daily times daily punch          5                                       5\r\n" );
document.write( "daily graphic daily punch                             20                20\r\n" );
document.write( "total                           70                    65                85\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "everything checks out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the number that applied to both daily times and daily graphic is 15 that applied to all three plus 10 that applied to daily times and daily graphic only.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "therefore, your solution is that the number that applied to daily time and daily graphic is 25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );