document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177493>Question 177493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having difficulty solving this: The pupils in a certain class are divided equally into 3 groups A, B and C.  The number of boys in A equals the number of girls in B.  25% of the boys in Class are in group C.  What is the ratio of boys to girls?\r<BR>\n" );
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document.write( "I know that A and B are split equally with boys and girls.  If group C has 25% of the boys that means the other 75% is split between the other 2 groups.  This is where I get lost.  Help please.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132559 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=132559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 3 groups.<BR>\n" );
document.write( "all 3 groups have the same number of students in them.<BR>\n" );
document.write( "let y = the number of students in each group.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "let b = total number of boys in all 3 groups.<BR>\n" );
document.write( "let g = total number of girls in all 3 groups.<BR>\n" );
document.write( "since y equals the total number of students in each group, this means that the total number of students in all 3 groups is 3*y.<BR>\n" );
document.write( "this also means that:<BR>\n" );
document.write( "b + g = 3*y<BR>\n" );
document.write( "---<BR>\n" );
document.write( "25% of the boys are in group C.<BR>\n" );
document.write( "this means .25*b are in group C.<BR>\n" );
document.write( "also means that 75% of the boys are in groups A and B.<BR>\n" );
document.write( "which means that .75*b are in groups A and B.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "let x = number of boys in A.<BR>\n" );
document.write( "that means the number of boys in B is equal to .75*b - x.<BR>\n" );
document.write( "if the number of boys in B is accurate, then the number of boys in A and the number of boys in B should total .75*b<BR>\n" );
document.write( "since x + .75*b - x = .75*b, this relationship holds and the number of boys in B is accurate.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the number of boys in A equals the number of girls in B.<BR>\n" );
document.write( "this means that the number of girls in B is equal to x.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "if the number of girls in B is x, and the number of boys in B is .75*b - x, and the total number of students in B is y, this means that:<BR>\n" );
document.write( ".75*b - x + x = y<BR>\n" );
document.write( "which means that:<BR>\n" );
document.write( ".75*b = y<BR>\n" );
document.write( "which means that:<BR>\n" );
document.write( "b = y/.75<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you also have that:<BR>\n" );
document.write( "b + g = 3*y<BR>\n" );
document.write( "substituting y/.75 for b in that equation, you get:<BR>\n" );
document.write( "y/.75 + g = 3*y<BR>\n" );
document.write( "subtract y/.75 from both sides of this equation to get:<BR>\n" );
document.write( "g = 3*y - y/.75<BR>\n" );
document.write( "which makes:<BR>\n" );
document.write( "g = 1.25*y/.75<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "b = y/.75<BR>\n" );
document.write( "g = 1.25*y/.75<BR>\n" );
document.write( "this makes:<BR>\n" );
document.write( "b + g = y/.75 + 1.25*y/.75 = 2.25*y/.75 = 3*y which is good because we already know that:<BR>\n" );
document.write( "b + g = 3*y<BR>\n" );
document.write( "the values of:<BR>\n" );
document.write( "b = y/.75<BR>\n" );
document.write( "g = 1.25*y/.75<BR>\n" );
document.write( "have been confirmed to be good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "since b = y/.75<BR>\n" );
document.write( "and g = 1.25*y/.75<BR>\n" );
document.write( "then the ratio of boys to girls must be:<BR>\n" );
document.write( "b/g = (y/.75)/(1.25*y/.75)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "b/g = y/.75 / (1.25*y)/.75) is the same as:<BR>\n" );
document.write( "b/g = y/.75 * (.75/1.25*y)<BR>\n" );
document.write( "the .75 cancels out and the y cancels out and we are left with:<BR>\n" );
document.write( "b/g = 1/1.25 which equals to .8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the ratio of boys to girls is .8<BR>\n" );
document.write( "---<BR>\n" );
document.write( " </SPAN>\n" );
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