We are given that the landlord needs to label all of the apartments from 100 through 125 on the first floor and 200 through $X$ on the second floor.
To determine the value of $X$, we can calculate the number of apartments on the second floor and add it to 200.
The number of apartments on the second floor can be found by subtracting the starting apartment number (200) from the ending apartment number ($X$) and adding 1 (to include both the starting and ending apartments).
So, the number of apartments on the second floor is $X - 200 + 1$.
Now, we can calculate the total number of apartments as the sum of the number of apartments on the first floor (26) and the number of apartments on the second floor ($X - 200 + 1$).
The total number of apartments is $26 + (X - 200 + 1)$.
We are given that the answer is 52, so we can write:
$52 = 26 + (X - 200 + 1)$
Simplifying, we have:
$52 = X - 173$
Adding 173 to both sides of the equation, we find:
$X = 225$
The value of $X$ is 225.
The answer is: 225
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The landlord of an apartment building needs to purchase enough digits to label all of the apartments from 100 through 125 on the first floor and 200 through X on the second floor. The digits can only be purchased in a package that contains one of each digit 0 through 9. How many packages must the landlord purchase?
If we know the answer to the above question is 52, what is the value of unknown variable X?

### Answer:
