calculating the fraction of professor 
For the biological sciences and health sciences faculty combined,
  $\frac13$ of the female and $\frac29$ of the male faculty members are
  tenured professors. What fraction of all the faculty members in those
  two fields combined are tenured professors?

Where I have done wrong. 

Let guess there are $x$ number of total faculty members  so we get the
  number of turned professor:  $\frac29 x+\frac13x$ so the resulting
  fraction will be: $$\frac{\frac{2}{9} x+\frac{1}{3}x}{x}$$

The answer is given as:

the answer will be $\frac{24}{87}$
 A: I would guess that there is additional information that you've not provided for us, namely, what fraction of faculty members in those two fields are (fe)male. Without knowing that, as André points out in the comments above, we cannot get a specific number. We can at least get the form of that number, however.
Suppose that $\alpha$ is the fraction of faculty members in those two fields that are female, so $1-\alpha$ is the fraction that are male (assuming there is no overlap and no other option). Then $\frac13\alpha$ is the fraction of faculty members in those two fields that are female and tenured, and $\frac29(1-\alpha)$ is the fraction of faculty members in those two fields that are male and tenured. Thus, the fraction of faculty members in those two fields that are tenured is $$\frac13\alpha+\frac29(1-\alpha)=\frac29+\frac19\alpha.$$ As $\alpha$ must range between $0$ and $1$ (inclusive) the best we can say is that the fraction is between $\frac29$ and $\frac13$ (inclusive), but at least we have the form.

Based on your edit, there was apparently a graph (or more) that was to lead to the conclusion that there were $42$ women and $45$ men. Using these numbers, $\alpha=\frac{42}{87}=\frac{14}{29},$ so the number is $$\frac29+\frac19\cdot\frac{14}{29}=\frac19\cdot\left(2+\frac{14}{29}\right)=\frac19\cdot\left(\frac{58}{29}+\frac{14}{29}\right)=\frac19\cdot\frac{72}{29}=\frac8{29},$$ which is the same as $\frac{24}{87}.$
A: Option 1: There are three women and nine men.  Then there are three tenured professors, out of 12, for $\frac14$.
Option 2: There are $30$ women and nine men.  Then there are $12$ tenured professors, out of 39, for a ration of $\frac{12}{39}>\frac14$.
As mentioned in the comments, this question cannot be answered without knowing the fraction of faculty that is male vs. female.  All we can know for sure is that the overall answer is somewhere between $\frac 13$ and $\frac 29$.
