document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220420>Question 220420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi - I got the answer to this by working it out but I cannot get to an equation. Can you help me?\r<BR>\n" );
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document.write( "A class has a boy-girl ratio of 5:3. Three more girls join the class, changing the ratio of 10:7. How many students are now in the class?\r<BR>\n" );
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document.write( "By trying and just plugging in numbers I got 30 and 18 plus 3 more, so now the total is 51 - but I'm not sure how to set it up as a problem!\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165486 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=165486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A class has a boy-girl ratio of 5:3. Three more girls join the class, changing the ratio of 10:7. How many students are now in the class?<BR>\n" );
document.write( "By trying and just plugging in numbers I got 30 and 18 plus 3 more, so now the total is 51 - but I'm not sure how to set it up as a problem!<BR>\n" );
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document.write( "let b = number of boys.<BR>\n" );
document.write( "let g = number of girls.<BR>\n" );
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document.write( "b/g = 5/3<BR>\n" );
document.write( "this means that b = 5g/3<BR>\n" );
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document.write( "add 3 girls and the ratio becomes 10/7<BR>\n" );
document.write( "this means that: <BR>\n" );
document.write( "b/(g+3) = 10/7<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "b = (10g + 30)/7<BR>\n" );
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document.write( "since both these equations equal to b, then they must equal to each other.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "5g/3 = (10g + 30)/7<BR>\n" );
document.write( "multiply both sides by 7 and you get:<BR>\n" );
document.write( "35g/3 = 10g + 30<BR>\n" );
document.write( "multiply both sides by 3 to get:<BR>\n" );
document.write( "35g = 30g + 90<BR>\n" );
document.write( "subtract 30g from both sides to get:<BR>\n" );
document.write( "5g = 90<BR>\n" );
document.write( "divide both sides by 5 to get:<BR>\n" );
document.write( "g = 18<BR>\n" );
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document.write( "original ratio led to bg = 5g/3<BR>\n" );
document.write( "5*18/3 = 5*6 = 30<BR>\n" );
document.write( "original class size is 30 boys and 18 girls.<BR>\n" );
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document.write( "add 3 girls and the class size is 30 boys and 21 girls.<BR>\n" );
document.write( "boy to girl ratio is now 30/21 which equals 10/7<BR>\n" );
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