<PRE><B>Question 1008112</B>

what is the sum of all integer values of x such that 31/90 &lt; x/100 &lt; 41/110 is true?

The answer is 108. How?
&lt;pre&gt;{{{31/90 &lt; x/100 &lt; 41/110}}}

{{{(3410/9900) &lt; (99x/9900) &lt; (3690/9900)}}}   ------------ Multiplying by LCD, 
It then becomes: {{{3410 &lt; 99x &lt; 3690}}}
{{{(3410/99) &lt; (99x/99) &lt; (3690/99)}}} --------- Dividing by 99
{{{34.444 &lt; x &lt; 37.27273}}}
Integers are therefore: {{{highlight_green(35 + 36 + 37 = 108)}}}</PRE>