In order to solve this, we must make 3 equations:

39 → number of male students

36 → number of female students

75 → total number of students

M_m= \frac{\text{Sum of all meals eaten by male (using m as a variable)}}{ \text{Number of male students}}

M_f= \frac{\text{Sum of all meals eaten by female (using f as a variable)}}{ \text{Number of female students}}

M_t= \frac{\text{Sum of all meals eaten by male and female}}{ \text{Number of total students}}

So, in our situation:

M_m= \frac{m}{39} = 2 \to m = 39 \cdot 2 \to m = 78.

M_t= \frac{m+f}{75} = 3 \frac{1}{5}= \frac{16}{5} \to m+f = 75 \cdot \frac{16}{5} = 240

\to f = 240-m = 240 - 78 \to f = 162.

Using that information, we can calculate the mean number of meals eaten by female students as:

M_f = \frac{f}{36} = \frac{162}{36} = \frac{81}{18} = \frac{9}{2} = 4\frac{1}{2}.

So the correct answer is **(A)**