document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220726>Question 220726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a word problem my son just had on a quiz and I couldn't solve either. I thought we didn't have enough info.\r<BR>\n" );
document.write( "\n" );
document.write( "Marshfield Middle school cluster C has 100 students in honors pre-algebra<BR>\n" );
document.write( "Cluster C has 30 students enrolled in after school math enrichment.\r<BR>\n" );
document.write( "\n" );
document.write( "If 105 cluster C students are in only one or the other of these, how many students are in both?\r<BR>\n" );
document.write( "\n" );
document.write( "Tried a venn diagram to get my mind around it, didn't work. (I keep thinking I need to know the total enrollment of honors pre-alg plus after school)my son said he got 12.5 as an answer, but the teacher said it would come out as a whole number.<BR>\n" );
document.write( "Thanks, Trish  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165630 by </B><A HREF=/tutors/aboutme.mpl?userid=kensson><B>kensson(21)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kensson><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=kensson><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=165630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I agree with your son, even if the answer doesn't make sense. I reckon the question is badly set up. \r<BR>\n" );
document.write( "\n" );
document.write( "Let's call the number of students in (only) honors pre-alg H, the number of students in (only) math enrichment M and the number in both B. We've got:\r<BR>\n" );
document.write( "\n" );
document.write( "1) H + B = 100<BR>\n" );
document.write( "2) B + M = 30<BR>\n" );
document.write( "3) H + M = 105\r<BR>\n" );
document.write( "\n" );
document.write( "1 + 2)  2B + H + M = 130<BR>\n" );
document.write( "1 + 2 - 3) 2B = 25\r<BR>\n" );
document.write( "\n" );
document.write( "B = 12.5\r<BR>\n" );
document.write( "\n" );
document.write( "Edit: I disagree with Jim's answer - his working would be correct if there were 105 students in Cluster C altogether.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );