<PRE><B>Question 1123204</B>
&lt;br&gt;
(1) Algebraically....&lt;br&gt;
We are asked to find the possible numbers of women on the committee, so use that as our variable; the number of men will be 3 less:&lt;br&gt;
let x = number of women
then x-3 = number of men&lt;br&gt;
The total number of people on the committee -- x, plus (x-3) -- is to be between 7 and 15:&lt;br&gt;
7 &lt;= x+(x-3) &lt;= 15
7 &lt;= 2x-3 &lt;= 15
10 &lt;= 2x &lt;= 18
5 &lt;= x &lt;= 9&lt;br&gt;
The number of women can be between 5 and 9.&lt;br&gt;
Using logical reasoning....&lt;br&gt;
Not counting the 3 &quot;extra&quot; women, the committee consists of equal numbers of men and women, and the total number on the committee is between 4 and 12; that means the numbers of men and women are between 4/2=2 and 12/2=6 each.  And then counting the other 3 women, the number of women is between 2+3=5 and 6+3=9.</PRE>