document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265919>Question 265919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a group of green monkeys, 10 females leave. At this point there are 3 males for every female. Then 25 males leave, at which point there are two males for every female. How many females were there originally? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195476 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK.\r<BR>\n" );
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document.write( "Let x=number of female green monkeys in the original group<BR>\n" );
document.write( "And let y=number of male green monkeys in the original group<BR>\n" );
document.write( "Then (x+y)=total number of monkeys in the original group\r<BR>\n" );
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document.write( "When 10 female green monkeys leave, we have left (x-10)+y monkeys remaining and we are basically told that 3/4 of this number are males, so:<BR>\n" );
document.write( "(3/4)((x-10)+y)=y multiply each side by 4<BR>\n" );
document.write( "3((x-10)+y)=4y get rid of parens<BR>\n" );
document.write( "3x-30+3y=4y subtract 4y and add 30 to each side<BR>\n" );
document.write( "3x-30+30+3y-4y=4y-4y+30  collect like terms\r<BR>\n" );
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document.write( "3x-y=30-----------------------------------------eq1\r<BR>\n" );
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document.write( "When 25 males leave, we have left(x-10)+(y-25) or (x+y-35) monkeys remaining and we are told that 2/3 of this number are males, so:<BR>\n" );
document.write( "(2/3)(x+y-35)=(y-25)  multiply each side by 3<BR>\n" );
document.write( "2(x+y-35)=3(y-25) get rid of parens<BR>\n" );
document.write( "2x+2y-70=3y-75 subtract 3y and add 70 to each side<BR>\n" );
document.write( "2x+2y-70+70-3y=3y-3y-75+70  collect like terms\r<BR>\n" );
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document.write( "2x-y=-5----------------------------------------eq2\r<BR>\n" );
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document.write( "subtract eq2 from eq1 and we get<BR>\n" );
document.write( "x=35------------------------------number of females originally<BR>\n" );
document.write( "substitute x=35 into eq 1 and we get:<BR>\n" );
document.write( "3*35-y=30<BR>\n" );
document.write( "105-y=30<BR>\n" );
document.write( "-y=-105+30=-75<BR>\n" );
document.write( "y=75 number of males originally\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "10 females leave:<BR>\n" );
document.write( "Number of females remaining:35-10=25<BR>\n" );
document.write( "Number of males: 75<BR>\n" );
document.write( "Total number of monkeys: 75+25=100<BR>\n" );
document.write( "75/100=3/4<BR>\n" );
document.write( "3/4=3/4<BR>\n" );
document.write( "25 males leave:<BR>\n" );
document.write( "Number of females remaining=25<BR>\n" );
document.write( "Number of males=75-25=50<BR>\n" );
document.write( "Total number of monkeys=50+25=75<BR>\n" );
document.write( "50/75=2/3<BR>\n" );
document.write( "2/3=2/3\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
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