<PRE><B>Question 1204109</B>
&lt;font color=black size=3&gt;
x = the number you are dividing over
It must be a positive number so that {{{(25.3)/(x)}}} is between the two positive numbers 10 and 11.


{{{10 &lt; (25.3)/(x) &lt; 11}}}


{{{10x &lt; x*((25.3)/(x)) &lt; 11x}}} Multiply all three sides by x. Multiplying all sides by a positive number does not flip the inequality signs.


{{{10x &lt; 25.3 &lt; 11x}}}


That last inequality breaks down into these two inequalities
{{{10x &lt; 25.3 }}} and {{{25.3 &lt; 11x }}}


Solve {{{10x &lt; 25.3 }}} to get {{{ x &lt; 2.53}}}


Solve {{{25.3 &lt; 11x }}} to get {{{x &gt; 2.3}}} aka {{{ 2.3 &lt; x}}}



We found that {{{ 2.3 &lt; x}}} and {{{ x &lt; 2.53}}}. 
Glue those together to get {{{2.3 &lt; x &lt; 2.53}}}



Here&#39;s a table of examples
&lt;table border = &quot;1&quot; cellpadding = &quot;5&quot;&gt;&lt;tr&gt;&lt;td&gt;x&lt;/td&gt;&lt;td&gt;(25.3)/x&lt;/td&gt;&lt;td&gt;Result greater than 10 but less than 11?&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.28&lt;/td&gt;&lt;td&gt;11.0965&lt;/td&gt;&lt;td&gt;no&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.3&lt;/td&gt;&lt;td&gt;11&lt;/td&gt;&lt;td&gt;no&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.32&lt;/td&gt;&lt;td&gt;10.9052&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.34&lt;/td&gt;&lt;td&gt;10.812&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.36&lt;/td&gt;&lt;td&gt;10.7203&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.38&lt;/td&gt;&lt;td&gt;10.6303&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.4&lt;/td&gt;&lt;td&gt;10.5417&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.42&lt;/td&gt;&lt;td&gt;10.4545&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.44&lt;/td&gt;&lt;td&gt;10.3689&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.46&lt;/td&gt;&lt;td&gt;10.2846&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.48&lt;/td&gt;&lt;td&gt;10.2016&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.5&lt;/td&gt;&lt;td&gt;10.12&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.52&lt;/td&gt;&lt;td&gt;10.0397&lt;/td&gt;&lt;td&gt;yes&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td&gt;2.54&lt;/td&gt;&lt;td&gt;9.9606&lt;/td&gt;&lt;td&gt;no&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;
With the exception of the results 11 and 10.12, each of the values in the 2nd column are approximate.


If we rounded to one decimal place, then the only possible x solutions would be: x = 2.4 and x = 2.5


x = 2.3 doesn&#39;t work since {{{10 &lt; (25.3)/(x) &lt; 11}}} becomes {{{10 &lt; (25.3)/(2.3) &lt; 11}}} and then simplifies to {{{10 &lt; 11 &lt; 11}}} which is false.


But x = 2.4 does work
{{{10 &lt; (25.3)/(x) &lt; 11}}} becomes {{{10 &lt; (25.3)/(2.4) &lt; 11}}} and then simplifies to {{{10 &lt; 10.54 &lt; 11}}} which is true


x = 2.5 also works as well
{{{10 &lt; (25.3)/(x) &lt; 11}}} becomes {{{10 &lt; (25.3)/(2.5) &lt; 11}}} and then simplifies to {{{10 &lt; 10.12 &lt; 11}}} which is true.




Answer: The mystery number is either 2.4 or 2.5
&lt;/font&gt;</PRE>