We want to find the value of $X$ in the given situation.
We are told that the 25th day of the year $X$ falls on a Saturday.
To determine the day of the week for the 284th day of the year 2003, we need to know the number of days between these two dates.
We can calculate the number of days by subtracting the 25th day of $X$ from the 284th day of 2003:
284 - 25 = 259
So, there are 259 days between the 25th day of $X$ and the 284th day of 2003.
Since there are 7 days in a week, we can divide 259 by 7 and find the remainder to determine the day of the week for the 284th day of 2003.
259 divided by 7 is 37 with a remainder of 0.
This means that the 284th day of 2003 falls on the same day of the week as the 25th day of $X$.
Given that the 25th day of $X$ falls on a Saturday, the 284th day of 2003 also falls on a Saturday.
Therefore, the value of $X$ does not affect the day of the week for the 284th day of 2003.
The answer is: 2003
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If the 25th day of the year X falls on a Saturday, on what day of the week did the 284th day of the year 2003 fall?
If we know the answer to the above question is \text{Saturday}, what is the value of unknown variable X?

### Answer:
