document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101086>Question 1101086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "a box contained 480 beads of 3 colors. When 18 yellow beads were added,33 orange beads were<BR>\n" );
document.write( "taken out and the number of black beads doubled, there were then an equal number of beads of <BR>\n" );
document.write( "Each color.\r<BR>\n" );
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document.write( "how many beads of each colour were there 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 #715693 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Answer:<BR>\n" );
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document.write( "Yellow:  168<BR>\n" );
document.write( "Orange: 219<BR>\n" );
document.write( "Black:     93<BR>\n" );
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document.write( "Check:  168 + 219 + 93 = 480<BR>\n" );
document.write( "   and:  168+18 = 186<BR>\n" );
document.write( "             219-33 = 186<BR>\n" );
document.write( "             2(93) = 186\r<BR>\n" );
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document.write( "—<BR>\n" );
document.write( "The workout starts from  <BR>\n" );
document.write( "480 = (Y - 18) + (O + 33) + (1/2)B    (where each letter = FINAL number of beads of that color)<BR>\n" );
document.write( "465 = Y + O + B   (*) <BR>\n" );
document.write( "and noting Y=O=B at this point, which gives   Y = O =  B = 186  (**)<BR>\n" );
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document.write( "Now to find the ORIGINAL number of each color bead, (using lower case y,o,b), just reverse the manipulations given in the problem statement:<BR>\n" );
document.write( "y = Y-18 = 186-18 = 168<BR>\n" );
document.write( "o = O+33 = 186+33 = 219<BR>\n" );
document.write( "b = (1/2)B = 186/2 = 93\r<BR>\n" );
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document.write( "——<BR>\n" );
document.write( " EDIT:  Dear student, I see why you are wondering how I got to Y=O=B=186.   The equation (* above) <BR>\n" );
document.write( "should have been written:<BR>\n" );
document.write( "                    480 = (Y-18) + (O+33) + (1/2)B<BR>\n" );
document.write( "                    465 = Y + O + (1/2)B<BR>\n" );
document.write( "and the three quantities that are equal are  Y = O = B   so\r<BR>\n" );
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document.write( "   465 = Y + Y + (1/2)Y = (5/2)Y  —> Y=186  <BR>\n" );
document.write( " and that means Y = O = B = 186.\r<BR>\n" );
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document.write( "Sorry, I had that step proper on paper but typed it wrong.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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