document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1038491>Question 1038491</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "kim had 580 red and green beads.<BR>\n" );
document.write( "after she gave 1/3 of the red beads, she bought another 80 green beads.<BR>\n" );
document.write( "now the number of green beads was half the number of red beads remaining. <BR>\n" );
document.write( "How many more red beads than green beads did she have at first. \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 #653201 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=653201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> kim had 580 red and green beads.<BR>\n" );
document.write( "after she gave 1/3 of the red beads, she bought another 80 green beads.<BR>\n" );
document.write( "now the number of green beads was half the number of red beads remaining. <BR>\n" );
document.write( "How many more red beads than green beads did she have at first. \r<BR>\n" );
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document.write( "let g equal the number of green beads.<BR>\n" );
document.write( "let r equal the number of red beads.\r<BR>\n" );
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document.write( "start with r + g = 580.\r<BR>\n" );
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document.write( "she gave away 1/3 of the red beads and added 80 to the green beads.<BR>\n" );
document.write( "this resulted in the green beads being equal to 1/2 of the remaining red beads.\r<BR>\n" );
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document.write( "the remaining red beads equal r - 1/3 * r = 2/3 * r\r<BR>\n" );
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document.write( "you get g + 80 = 1/2 * 2/3 * r\r<BR>\n" );
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document.write( "you have 2 equations that needs to be solved simultaneously.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "r + g = 580<BR>\n" );
document.write( "g + 80 = 1/2 * 2/3 * r\r<BR>\n" );
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document.write( "simplify the second equation to get g + 80 = 1/3 * r.<BR>\n" );
document.write( "solve for g to get g = 1/3 * r - 80.\r<BR>\n" );
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document.write( "replace g in the first equation of r + g = 580 with its equivalent value of 1/3 * r - 80 to get r + 1/3 * r - 80 = 580.<BR>\n" );
document.write( "simplify to get 4/3 * r - 80 = 580.<BR>\n" );
document.write( "add 80 to both sides to get 4/3 * r = 660<BR>\n" );
document.write( "multiply both sides by 3/4 to get r = 3/4 * 660 = 495.\r<BR>\n" );
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document.write( "since r + g = 580 and r = 495, then g must be equal to 85, because 495 + 85 = 580. \r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "r = 495<BR>\n" );
document.write( "g = 85.\r<BR>\n" );
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document.write( "r + g = 580 becomes 495 + 85 = 580 which becomes 580 = 580.<BR>\n" );
document.write( "this confirms the solution satisfies this part of the problem statement.\r<BR>\n" );
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document.write( "g + 80 = 1/2 * 2/3 * r becomes 85 + 80 = 1/2 * 2/3 * 495 which becomes 165 = 165.<BR>\n" );
document.write( "this confirms the solution satisfies this part of the problem statement.\r<BR>\n" );
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document.write( "the solution is.....\r<BR>\n" );
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document.write( "number of red beads was originally 495 and number of green beads was originally 85.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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