document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185209>Question 1185209</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a box, there was a total of 2 353 blue and black marbles. Oliver took 3/7 of the blue<BR>\n" );
document.write( "marbles and 455 of the black marbles. After that, the number of blue marbles left was 2/3<BR>\n" );
document.write( "the number of black marbles left. How many black marbles were there in the box at first?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815993 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from tutor @ikleyn shows a straightforward setup and solution for the problem.<br><BR>\n" );
document.write( "I decided to just try a very different setup to see if the path to the solution was any easier....<br><BR>\n" );
document.write( "After Oliver took 3/7 of the blue marbles, 4/7 of them were left; those 4/7 of the blue marbles were 2/3 of the number of black marbles left.<br><BR>\n" );
document.write( "To use \"nice\" numbers, then, let the number of blue marbles left after Oliver took some be 4x; then the number of black marbles left was 6x.  So<br><BR>\n" );
document.write( "4x = blue marbles left<BR>\n" );
document.write( "6x = black marbles left<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "7x = blue marbles originally<BR>\n" );
document.write( "6x+455 = black marbles originally<br><BR>\n" );
document.write( "The total number of marbles originally was 2353:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B6x%2B455=2353 ALIGN=MIDDLE  ALT=\"7x%2B6x%2B455=2353\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x=1898 ALIGN=MIDDLE  ALT=\"13x=1898\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1898%2F13=146 ALIGN=MIDDLE  ALT=\"x=1898%2F13=146\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS: The numbers of marbles in the box originally were<BR>\n" );
document.write( "blue: 7x = 7(146) = 1022<BR>\n" );
document.write( "black: 6x+455 = 6(146)+455 = 1331<br><BR>\n" );
document.write( "The algebra ended up being easier than with the solution shown by the other tutor; but it took more time to figure out how to set the problem up....<br><BR>\n" );
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document.write( "The point of my response:<br><BR>\n" );
document.write( "Never be afraid of looking at different ways of doing things -- that's how progress is made.<br><BR>\n" );
document.write( "(If we never looked for better ways to do things, we would still all be living in caves....)<br><BR>\n" );
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