document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176896>Question 1176896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "A and B  had some cards. After A lost 68 cards to B the ratio of cards that A and B had were 3:8 respectively. When B lost 126 cards to A the ratio of cards that A and B had were 2:3 respectively. <BR>\n" );
document.write( "How many cards did A have at first. <BR>\n" );
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 #805395 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=805395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> my interpretation of this problem is:\r<BR>\n" );
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document.write( "A and B had some cards.<BR>\n" );
document.write( "After A lost 68 cards to B, the ratio of cards that A had to B was 3/8.<BR>\n" );
document.write( "When B subsequently lost 126 cards to A, the ratio of cards that A had to B became 2/3.\r<BR>\n" );
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document.write( "the first part of this problem became:\r<BR>\n" );
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document.write( "(A - 68) / (B + 68) = 3/8\r<BR>\n" );
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document.write( "the second part of this problem became:\r<BR>\n" );
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document.write( "(A + 58) / (B - 58) = 2/3.\r<BR>\n" );
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document.write( "the reason for this is that A first lost 68 cards and then won 126 cards, giving him a net gain of 58 cards and that B first won 68 cards and then lost 126 cards, giving him a net loss of 58 cards.\r<BR>\n" );
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document.write( "you have two 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( "(A - 68) / (B + 68) = 3/8<BR>\n" );
document.write( "(A + 58) / (B - 58) = 2/3\r<BR>\n" );
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document.write( "in the first equation, you get:<BR>\n" );
document.write( "(A - 68) = 3/8 * (B + 68)<BR>\n" );
document.write( "solve for A to get:<BR>\n" );
document.write( "A = 3/8 * (B + 68) + 68.\r<BR>\n" );
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document.write( "in the second equation, you get:<BR>\n" );
document.write( "(A + 58) = 2/3 * (B - 58)<BR>\n" );
document.write( "solve for A to get:<BR>\n" );
document.write( "A = 2/3 * (B - 58) - 58\r<BR>\n" );
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document.write( "since they are both equal to A, you get:\r<BR>\n" );
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document.write( "3/8 * (B + 68) + 68 = 2/3 * (B - 58) - 58\r<BR>\n" );
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document.write( "subtract 3/8 * (B + 68) from both sides of the equation and add 58 to both sides of the equation to get:\r<BR>\n" );
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document.write( "68 + 58 = 2/3 * (B - 58) - 3/8 * (B + 68)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "126 = 2/3 * B - 2/3 * 58 - 3/8 * B - 3/8 * 68\r<BR>\n" );
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document.write( "add 2/3 * 58 and 3/8 * 68 to both sides of the equation to get:\r<BR>\n" );
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document.write( "126 + 2/3 * 58 + 3/8 * 68 = 2/3 * B - 3/8 * B\r<BR>\n" );
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document.write( "put everything under the common denominator of 24 to get:\r<BR>\n" );
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document.write( "3024 / 24 + 928 / 24 + 612 / 24 = 16/24 * b - 9/24 * B\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "4564 / 24 = 7/24 * B\r<BR>\n" );
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document.write( "solve for B to get:\r<BR>\n" );
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document.write( "B = 24/7 * 4564 / 24 = 652.\r<BR>\n" );
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document.write( "since A = 3/8 * (B + 68) + 68, then:\r<BR>\n" );
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document.write( "A = 3/8 * (652 + 68) + 68 = 338.\r<BR>\n" );
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document.write( "when A = 338 and B = 652:\r<BR>\n" );
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document.write( "(A - 68) / B + 68) becomes (338 - 68) / (652 + 68) = 270 / 720 = 3/8.\r<BR>\n" );
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document.write( "(A + 58) / (B - 58) becomes (338 + 58) / (652 - 58) = 396 / 594 = 2/3.\r<BR>\n" );
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document.write( "the requirements of the problem are satisfied.\r<BR>\n" );
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document.write( "your answer is that A had 338 cards at first.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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