document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763406>Question 763406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alice and Bob each have a certain amount of money. If Alice receives  dollars from Bob, then she will have 3 times as much money as Bob. If, on the other hand, she gives  dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464856 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=464856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alice and Bob each have a certain amount of money.<BR>\n" );
document.write( " If Alice receives dollars from Bob, then she will have 3 times<BR>\n" );
document.write( " as much money as Bob. <BR>\n" );
document.write( "If, on the other hand, she gives dollars to Bob, then she will have 2<BR>\n" );
document.write( " times as much money as Bob.<BR>\n" );
document.write( " If neither gives the other any money, what is the ratio of the amount<BR>\n" );
document.write( " of money Alice has to the amount Bob has?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let A = Alice's original amt of money<BR>\n" );
document.write( "Let B = Bob's original amt of money<BR>\n" );
document.write( "Let d = the dollars they are referring to<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement, simplify:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If Alice receives dollars from Bob, then she will have 3 times as much money as Bob.\"<BR>\n" );
document.write( "A + d = 3(B-d)<BR>\n" );
document.write( "A + d = 3B - 3d<BR>\n" );
document.write( "A = 3B - 3d - d<BR>\n" );
document.write( "A = 3B - 4d<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"she gives dollars to Bob, then she will have 2 times as much money<BR>\n" );
document.write( " as Bob.\"<BR>\n" );
document.write( "A - d = 2(b+d)<BR>\n" );
document.write( "A - d = 2B + 2d<BR>\n" );
document.write( "A = 2B + 2d + d<BR>\n" );
document.write( "A = 2B + 3d<BR>\n" );
document.write( "A = A; therefore<BR>\n" );
document.write( "3B - 4d  = 2B + 3d<BR>\n" );
document.write( "3B - 2B = 3d + 4d<BR>\n" );
document.write( "B = 7d<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find A in terms of d also,<BR>\n" );
document.write( "A = 2B + 3d<BR>\n" );
document.write( "Replace B with 7d<BR>\n" );
document.write( "A = 2(7d) + 3d<BR>\n" );
document.write( "A = 17d<BR>\n" );
document.write( "\"neither gives the other any money, what is the ratio of the amount<BR>\n" );
document.write( " of money Alice has to the amount Bob has?\"<BR>\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2FB ALIGN=MIDDLE  ALT=\"A%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace A and B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817d%29%2F%287d%29 ALIGN=MIDDLE  ALT=\"%2817d%29%2F%287d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel d<BR>\n" );
document.write( "A:B ratio: 17:7<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );