<PRE><B>Question 1109226</B>
&lt;br&gt;
You undoubtedly posed the question incorrectly.  The way you stated the problem, there are an infinite number of answers.&lt;br&gt;
But if you state the problem correctly, by saying that the two numbers are integers, then there is only one answer.&lt;br&gt;
Let the smaller number be x; then, since the sum of the two numbers is 11, the larger is 11-x.&lt;br&gt;
The problem tells us that when 11-x is divided by x, the whole number part of the answer is 2.  So 11-x divided by x must be between 2 and 3:&lt;br&gt;
{{{2 &lt; (11-x)/x &lt; 3}}}
{{{2x &lt; 11-x &lt; 3x}}}  (we don&#39;t need to worry about multiplying by x, because we know x is positive)
{{{2x &lt; 11-x}}}  and  {{{11-x &lt; 3x}}}
{{{3x &lt; 11}}} and {{{11 &lt; 4x}}}
{{{x &lt; 11/3}}} and {{{x &gt; 11/4}}}
{{{11/4 &lt; x &lt; 11/3}}}&lt;br&gt;
There are of course an infinite number of values of x between 11/4 (2 3/4) and 11/3 (3 2/3).  But there is only one integer, 3 between those two numbers.&lt;br&gt;
So the smaller number, x, is 3; the larger number is 11-x = 11-3 = 8.&lt;br&gt;
Checking, we see when 8 is divided by 3 the whole number part of the quotient is 2, as required.</PRE>