document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=966312>Question 966312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2 people had 270$ altogether. one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money. How much did they each have at first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590587 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=590587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  2 people had 270$ altogether. one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money.<BR>\n" );
document.write( " How much did they each have at first?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = amt one person has originally<BR>\n" );
document.write( "let b = amt the other person has<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "a + b = 270<BR>\n" );
document.write( "a = (270-b)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money.\"<BR>\n" );
document.write( "a - .25a + .33b = b - .33b + .25a<BR>\n" );
document.write( ".75a + .33b = .67b + .25a<BR>\n" );
document.write( ".75a - .25a = .67b - .33b<BR>\n" );
document.write( ".50a = .33b<BR>\n" );
document.write( "replace a with (270-b)<BR>\n" );
document.write( ".50(270-b) = .33b<BR>\n" );
document.write( "135 - .5b = .33b<BR>\n" );
document.write( "135 = .33b + .5b<BR>\n" );
document.write( "135 = .83b<BR>\n" );
document.write( "b = 135/.83<BR>\n" );
document.write( "b = $162.65 b's amt<BR>\n" );
document.write( "then <BR>\n" );
document.write( "270 - 162.65 = $107.35 a's amt<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if they have the same amt<BR>\n" );
document.write( ".75(107.35) + .33(162.65)  = 134.76<BR>\n" );
document.write( "and<BR>\n" );
document.write( ".667(162.65) + (.25(107.35) = 135.33; is that close enough?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );