In the equation $y = 50 + 10x$, which models the number of books in the library, the number 50 represents the initial number of books donated. This is because Carlos started with 50 books before adding more each month.

The answer is: "The initial number of books donated."

Would you like more details or have any further questions?

Here are some related questions you might consider:

1. What does the number 10 represent in this equation?
2. How would the equation change if 15 books were added each month instead of 10?
3. What would the equation look like if Carlos received 100 initial books?
4. After how many months will there be 150 books in the library?
5. If Carlos stopped adding new books after 6 months, what would the equation become?

Tip: When interpreting a linear equation, the constant term often represents an initial value or starting point, while the coefficient of $x$ shows how something changes over time.