<PRE><B>Question 1185209</B>
&lt;br&gt;
The response from tutor @ikleyn shows a straightforward setup and solution for the problem.&lt;br&gt;
I decided to just try a very different setup to see if the path to the solution was any easier....&lt;br&gt;
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.&lt;br&gt;
To use &quot;nice&quot; 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&lt;br&gt;
4x = blue marbles left
6x = black marbles left&lt;br&gt;
Then&lt;br&gt;
7x = blue marbles originally
6x+455 = black marbles originally&lt;br&gt;
The total number of marbles originally was 2353:&lt;br&gt;
{{{7x+6x+455=2353}}}
{{{13x=1898}}}
{{{x=1898/13=146}}}&lt;br&gt;
ANSWERS: The numbers of marbles in the box originally were
blue: 7x = 7(146) = 1022
black: 6x+455 = 6(146)+455 = 1331&lt;br&gt;
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....&lt;br&gt;
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The point of my response:&lt;br&gt;
Never be afraid of looking at different ways of doing things -- that&#39;s how progress is made.&lt;br&gt;
(If we never looked for better ways to do things, we would still all be living in caves....)&lt;br&gt;
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