document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082382>Question 1082382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a High school there are two Form 5 classes with the same number of students <BR>\n" );
document.write( "in each. The ratio of girls to boys in one Form 5 is 1 : 2 and in the other Form it is 3 : 2. What is the ratio of girls to boys in the entire Form 5?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696443 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=696443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you've got 2 form 5 classes with the same number of students in each class.\r<BR>\n" );
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document.write( "the ratio of girls to boys in each class is:\r<BR>\n" );
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document.write( "first form 5 class = 1:2<BR>\n" );
document.write( "second form 5 class = 3:2\r<BR>\n" );
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document.write( "a ratio of 1:2 means that there is 1 girl for every 2 boys in the first form 5 class.   <BR>\n" );
document.write( "this means that there is 1 girl out of 3 students in the first form 5 class.\r<BR>\n" );
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document.write( "a ratio of 3:2 means that there are 3 girls for every 2 boys in the second form class.   <BR>\n" );
document.write( "this means that there are 3 girls out of 5 students in the second form class.\r<BR>\n" );
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document.write( "therefore the ratio of girls to students in the first form 5 class is 1/3.<BR>\n" );
document.write( "therefore the ratio of girls to students in the second form 5 class is 3/5.\r<BR>\n" );
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document.write( "if you let x equal the number of students in each class, then:\r<BR>\n" );
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document.write( "the number of girls in the first form 5 class is 1/3 * x.<BR>\n" );
document.write( "the number of girls in the second form 5 class is 3/5 * x.\r<BR>\n" );
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document.write( "the total number of students in both classes is 2x.<BR>\n" );
document.write( "the total number of girls in both classes is 1/3 * x + 3/5 * x.\r<BR>\n" );
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document.write( "1/3 is equivalent to 5/15.<BR>\n" );
document.write( "3/5 is equivalent to 9/15.\r<BR>\n" );
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document.write( "the total number of girls in both classes is therefore equal to 5/15 * x + 9/15 * x = 14/15 * x.\r<BR>\n" );
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document.write( "since the total number of students in both classes is equal to 2x, then:\r<BR>\n" );
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document.write( "the ratio of girls to students in both classes is equal to (14/15 * x) / 2x.<BR>\n" );
document.write( "simplify to get the ratio of girls to students in both classes is equal to 7/15 * x.\r<BR>\n" );
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document.write( "this means that there are 7 girls for every 15 students.<BR>\n" );
document.write( "this means that 8 of those 15 students have to be boys.\r<BR>\n" );
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document.write( "the ratio of girls to boys in both classes is therefore 7/8.\r<BR>\n" );
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document.write( "to see if this makes sense, let's use numbers.\r<BR>\n" );
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document.write( "assume the number of students in each class is 45.<BR>\n" );
document.write( "this means the number of students in both classes is 90.\r<BR>\n" );
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document.write( "in the first form 5 class, the ratio of girls to boys is 1:2.<BR>\n" );
document.write( "this means that there is 1 girl for every 3 students and 2 boys for every 3 students.<BR>\n" );
document.write( "divide 45 by 3 and you get 15.<BR>\n" );
document.write( "this means you have 15 groups of 3 in the first form 5 class.<BR>\n" );
document.write( "within each of these groups of 3, 1 of them are girls and 2 of them are boys.<BR>\n" );
document.write( "this means in the total class of 45 you have 1 * 15 = 15 girls and 2 * 15 = 30 boys.\r<BR>\n" );
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document.write( "in the second form 5 class the ratio of girls to boys is 3:2.<BR>\n" );
document.write( "this means that there are 3 girls for every 5 students and 2 boys for every 5 students.<BR>\n" );
document.write( "divide 45 by 5 and you get 9.<BR>\n" );
document.write( "this means you have 9 groups of 5 in the second form 5 class.<BR>\n" );
document.write( "within each of these groups of 5, 3 are girls and 2 are boys.<BR>\n" );
document.write( "this means in the total class of 45 you have 3 * 9 = 27 girls and 2 * 9 = 18 boys.\r<BR>\n" );
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document.write( "in the first class you have 15 girls and 30 boys.<BR>\n" );
document.write( "in the second class you have 27 girls and 18 boys.\r<BR>\n" );
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document.write( "the total girls in both classes is 15 + 27 = 42.<BR>\n" );
document.write( "the total boys in both classes is 30 + 18 = 48.\r<BR>\n" );
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document.write( "the ratio of girls to boys in both classes is 42/48 = 21/24 = 7/8.\r<BR>\n" );
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document.write( "looks like we calculated the ratio correctly since this agrees with what we got before.\r<BR>\n" );
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document.write( "the ratio of girls to students in both classes would be 42/90 = 21/45 = 7/15.\r<BR>\n" );
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document.write( "this also agrees with what we got earlier when we were using x instead of 45.\r<BR>\n" );
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document.write( "your solution is that the ratio of girls to boys in the entire form 5 class is 7:8.\r<BR>\n" );
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document.write( "there are 7 girls for every 8 boys in both classes.\r<BR>\n" );
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