There are 25 students total, took Math and Science; 17 passed both, and 8 passed only Mathematics? How many passed Mathematics?

Let $U$ be the set of all students, $M$ be the set of students who passed Mathematics, and $S$ be the set of students who passed Science.
We are given:

• Total number of students, $|U| = 25$
• Number of students who passed Science, $|S| = 17$
• Number of students who passed both Mathematics and Science, $|M \cap S| = 8$

This is the number of students in set $S$ but not in set $M$.

$$|S \text{ only}| = |S| - |M \cap S| = 17 - 8 = 9$$

The problem implies that all students took Math and Science, and the student's calculation $17+T=25$ suggests that no students passed neither subject. Therefore, the total number of students is equal to the number of students who passed at least one subject.
Let $|M \text{ only}|$ be $x$.
The total number of students is the sum of those who passed only Math, only Science, and both:

$$|U| = |M \text{ only}| + |S \text{ only}| + |M \cap S|$$ $$25 = x + 9 + 8$$ $$25 = x + 17$$ $$x = 25 - 17 = 8$$

So, 8 students passed only Mathematics. (This matches your calculated value for $T$).

The question asks "How many Passed Mathematics?". This includes students who passed only Mathematics and those who passed both Mathematics and Science.

$$|M| = |M \text{ only}| + |M \cap S|$$ $$|M| = 8 + 8 = 16$$

The total number of students who passed Mathematics is $\text{16}$.