The following table shows the frequency distribution of the ages of 100 persons: Ages (in years) | Frequency 15-25 | 6 25-35 | x 35-45 | 7 45-55 | 4 55-65 | 5 If the mode of the distribution is 39, fi

The given mode is 39. Since 39 falls in the class interval 35-45, this is our modal class.
The formula for the mode of grouped data is:

Where:
$L$ = lower limit of the modal class
$h$ = size of the class interval
$f_1$ = frequency of the modal class
$f_0$ = frequency of the class preceding the modal class
$f_2$ = frequency of the class succeeding the modal class

From the modal class 35-45:
$L = 35$
$h = 45 - 35 = 10$
$f_1 = 7$ (frequency of 35-45)
$f_0 = x$ (frequency of 25-35)
$f_2 = 4$ (frequency of 45-55)
The given mode is 39.

First, subtract 35 from both sides:

Divide both sides by 10:

Cross-multiply:

Rearrange the terms to solve for $x$:

The value of the unknown frequency $x$ is $\boxed{\text{5}}$.