document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122788>Question 1122788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "joanne and dave each plucked a certain number of oranges in an orchard. Joanne gave 1/5 of her orange s to dave. Dave then gzve 1/6 of what he had back to her. Next joanne gave 1/3 back to dave. At the end joanne had 36 orange s and dave 88.\r<BR>\n" );
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document.write( "how many did easch of yhem pluck initially. \r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738963 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=738963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> joanne had 50 to start.<BR>\n" );
document.write( "dave had 74 to start.\r<BR>\n" );
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document.write( "joanne gave 1/5 of what she had to dave.<BR>\n" );
document.write( "1/5 of 50 = 10\r<BR>\n" );
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document.write( "joanne now had 40<BR>\n" );
document.write( "dave now had 84.\r<BR>\n" );
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document.write( "dave gave 1/6 of what he had back to joanne.<BR>\n" );
document.write( "1/6 of 84 = 14\r<BR>\n" );
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document.write( "joanne now had 54<BR>\n" );
document.write( "dave now had 70\r<BR>\n" );
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document.write( "joanne gave 1/3 of what she had back to dave.<BR>\n" );
document.write( "1/3 of 54 = 18.\r<BR>\n" );
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document.write( "joanne now had 36<BR>\n" );
document.write( "dave now had 88.\r<BR>\n" );
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document.write( "solution looks good.<BR>\n" );
document.write( "solution is that joanne plucked 50 originally and dave plucked 74 originally.\r<BR>\n" );
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document.write( "you can work forwards or you can work back.<BR>\n" );
document.write( "either way is a chore.\r<BR>\n" );
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document.write( "i worked forward as follows:\r<BR>\n" );
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document.write( "let A = the amount of oranges that joanne had originally and let B = the amount of oranges that dave had originally.\r<BR>\n" );
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document.write( "step 1:\r<BR>\n" );
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document.write( "joanne gave 1/5 of her oranges to dave.\r<BR>\n" );
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document.write( "joanne now had 4/5 * A\r<BR>\n" );
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document.write( "dave now had B + 1/5 * A\r<BR>\n" );
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document.write( "step 2:\r<BR>\n" );
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document.write( "dave gave 1/6 of what he had back to joanne.\r<BR>\n" );
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document.write( "joanne now had 4/5 * A + 1/6 * (B + 1/5 * A)<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "joanne now had 4/5 * A + 1/6 * B + 1/6 * 1/5 * A<BR>\n" );
document.write( "simlify further to get:<BR>\n" );
document.write( "joanne now had 4/5 * A + 1/6 * B + 1/30 * A<BR>\n" );
document.write( "4/5 * A is equivalent to 24/30 * A<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "joanne now had 24/30 * A + 1/6 * B + 1/30 * A<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "joanne now had 25/30 * A + 1/6 * B\r<BR>\n" );
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document.write( "dave now had B + 1/5 * A - 1/6 * (B + 1/5 * A)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "dave now had B + 1/5 * A - 1/6 * B - 1/6 * 1/5 * A<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "dave now had 5/6 * B + 1/5 * A - 1/30 * A<BR>\n" );
document.write( "1/5 * A is equivalent to 6/30 * A<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "dave now had 5/6 * B + 6/30 * A - 1/30 * A<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "dave now had 5/6 * B + 5/30 * A\r<BR>\n" );
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document.write( "step 3:\r<BR>\n" );
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document.write( "joanne gave 1/3 of what she had back to dave.\r<BR>\n" );
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document.write( "joanne now had 25/30 * A + 1/6 * B - 1/3 * (25/30 * A + 1/6 * B)<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "joanne now had 25/30 * A + 1/6 * B - 1/3 * 25/30 * A - 1/3 * 1/6 * B<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "joanne now had 25/30 * A + 1/6 * B - 25/90 * A - 1/18 * B<BR>\n" );
document.write( "25/30 * A is equivalent to 75/90 * A<BR>\n" );
document.write( "1/6 * B is equivalent to 3/18 * B<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "joanne now had 75/90 * A + 3/18 * B - 25/90 * A - 1/18 * B<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "joanne now had 50/90 * A + 2/18 * B\r<BR>\n" );
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document.write( "dave now had 5/6 * B + 5/30 * A + 1/3 * (25/30 * A + 1/6 * B)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "dave now had 5/6 * B + 5/30 * A + 25/90 * A + 1/18 * B<BR>\n" );
document.write( "5/6 * B is equivalent to 15/18 * B<BR>\n" );
document.write( "5/30 * A is equivalent to 15/90 * A<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "dave now had 15/18 * B + 15/90 * A + 25/90 * A + 1/18 * B<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "dave now had 16/18 * B + 40/90 * A\r<BR>\n" );
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document.write( "step 4.\r<BR>\n" );
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document.write( "joanne ended up with 36.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "50/90 * A + 2/18 * B = 36\r<BR>\n" );
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document.write( "dave ended up with 88.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "16/18 * B + 40/90 * A = 88\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "50/90 * A + 2/18 * B = 36<BR>\n" );
document.write( "16/18 * B + 40/90 * A = 88\r<BR>\n" );
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document.write( "rearrange the terms so that like terms are underneath each other.\r<BR>\n" );
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document.write( "equations become:\r<BR>\n" );
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document.write( "50/90 * A + 2/18 * B = 36<BR>\n" );
document.write( "40/90 * A + 16/18 * B = 88\r<BR>\n" );
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document.write( "multiply both sides of both equations by 90 to get:\r<BR>\n" );
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document.write( "50 * A + 10 * B = 3240<BR>\n" );
document.write( "40 * A + 80 * B = 7920\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 8 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "400 * A + 80 * B = 25920<BR>\n" );
document.write( "40 * A + 80 * B = 7920\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "360 * A = 18000\r<BR>\n" );
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document.write( "solve for A to get:\r<BR>\n" );
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document.write( "A = 18000 / 360 = 50\r<BR>\n" );
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document.write( "in the second equation of 40 * A + 80 * B = 7920, replace A with 50 to get:<BR>\n" );
document.write( "40 * 50 + 80 * B = 7920<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "2000 + 80 * B = 7920<BR>\n" );
document.write( "subtract 2000 from both sides of this equation to get:<BR>\n" );
document.write( "80 * B = 5920<BR>\n" );
document.write( "solve for B to get:<BR>\n" );
document.write( "B = 5920 / 80 = 74.\r<BR>\n" );
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document.write( "your solution is that A = 50 and B = 74 which means that:\r<BR>\n" );
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document.write( "joanne started with 50 and dave started with 74.\r<BR>\n" );
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document.write( "this was already confirmed to be a good solution.\r<BR>\n" );
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document.write( "as i said before, it's a chore.<BR>\n" );
document.write( "you have to be very diligent about keeping track of what you're doing.<BR>\n" );
document.write( "you could also work your way back from the answer, but that's also a chore.<BR>\n" );
document.write( "which one is easier is up for grabs.<BR>\n" );
document.write( "try it both ways and see which one you like better.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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