document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040489>Question 1040489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an art class, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the students are girls and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of girls are seniors. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of senior girls have passed the final art test, which of the following could be the number of students in this class?.<BR>\n" );
document.write( "A) 20<BR>\n" );
document.write( "B) 30<BR>\n" );
document.write( "C) 45<BR>\n" );
document.write( "D) 60 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655307 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=655307\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you need to test each one out to see which ones are possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the total is 20, and 2/3 are girls, then the number of girls is 20 * 2/3 = 13 and 1/3 which is not possible, so it can't be 20.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the total is 30, and 2/3 are girls, then the number of girls is 20 which is possible.   <BR>\n" );
document.write( "if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 20 = 40/5 = 8 which is possible.  <BR>\n" );
document.write( "if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 8 = 8/3 which is equal to 2 and 2/3 which is not possible, so it can't be 30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the total is 45, and 2/3 are girls, then the number of girls is 30 which is possible.<BR>\n" );
document.write( "if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 30 = 12 which is possible.<BR>\n" );
document.write( "if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 12 = 4 which is possible, so a total of 45 is possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the total is 60, and 2/3 are girls, then the number of girls is 40 which is possible.<BR>\n" );
document.write( "if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 40 = 16 which is possible.<BR>\n" );
document.write( "if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 16 = 5 and 1/3 which is not possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the only possible number of students is therefore 45.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could also have done this algebraically as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let g = number of girls.<BR>\n" );
document.write( "let t = total number of students.<BR>\n" );
document.write( "2/3 of the students are girls.<BR>\n" );
document.write( "you get g = 2/3 * t.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2/5 of the girls are seniors.<BR>\n" );
document.write( "let s = number of seniors.<BR>\n" );
document.write( "you get 2/5 * g = s<BR>\n" );
document.write( "since g = 2/3 * t, you get 2/5 * 2/3 * t = s<BR>\n" );
document.write( "simplify to get 4/15 * t = s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let p = number of senior girls who passed the final<BR>\n" );
document.write( "you get p = 1/3 * s<BR>\n" );
document.write( "since s = 4/15 * t, you get 1/3 * 4/15 * t = p<BR>\n" );
document.write( "simplify to get 4/45 * t = p\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can use this last formula to determine what the number of t could be.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if t = 20, then 4/45 * 20 = p which results in p = 1.78 which is not possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if t = 30, then 4/45 * 30 = p which result in p = 2.67 which is not possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if t = 45, then 4/45 * 45 = 4 which is possible *****\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if t = 60, then 4/45 * 60 = 5.33 which is not possible.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the only possible situation that results in p being equal to an integer is when the total number of student = 45, so that has to be your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );