document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984473>Question 984473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A, B and C are three groups of pupils. If group A is 1/3 of the total number of pupils in the three groups, Group B has 5 pupils more than group A and group C has 3/5 as many pupils as group B, find the original number of pupils in each group. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605314 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A, B and C are three groups of pupils. If group A is 1/3 of the total number of pupils in the three groups, Group B has 5 pupils more than group A and group C has 3/5 as many pupils as group B, find the original number of pupils in each group.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( "\" group A is 1/3 of the total number of pupils in the three groups,\"<BR>\n" );
document.write( "a = <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;\" >(a+b+c)<BR>\n" );
document.write( "3a = a + b + c (multiplied both sides by 3)<BR>\n" );
document.write( "3a - a = b + c<BR>\n" );
document.write( "2a = b + c<BR>\n" );
document.write( "\" Group B has 5 pupils more than group A\"<BR>\n" );
document.write( "b = a + 5<BR>\n" );
document.write( "or<BR>\n" );
document.write( "a = b - 5<BR>\n" );
document.write( "\"group C has 3/5 as many pupils as group B,\"<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >b<BR>\n" );
document.write( "c = .6b (decimals will work here)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "In the 1st equation, 2a = b + c, replace c with .6b and replace a with (b-5)<BR>\n" );
document.write( "2(b-5) = b + .6b<BR>\n" );
document.write( "2b - 10 = 1.6b<BR>\n" );
document.write( "2b - 1.6b = 10<BR>\n" );
document.write( ".4b = 10<BR>\n" );
document.write( "b = 10/.4<BR>\n" );
document.write( "b = 25<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 25 - 5<BR>\n" );
document.write( "a = 20<BR>\n" );
document.write( "and<BR>\n" );
document.write( "c = .6(25)<BR>\n" );
document.write( "c = 15<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the original number of pupils in each group.<BR>\n" );
document.write( "a = 20; b = 25 ; c = 15<BR>\n" );
document.write( ":<BR>\n" );
document.write( ";<BR>\n" );
document.write( "See if that checks out in the 1st statement<BR>\n" );
document.write( " group A is 1/3 of the total number of pupils in the three groups,\"<BR>\n" );
document.write( "20 = <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;\" >(20+25+15)<BR>\n" );
document.write( "20 = <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;\" >(60) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );