Solve a(a+4) vs a² in Exam Statistics: Finding Total Class Size

To solve the problem, we start by establishing the given conditions:

• More students passed than failed, and the difference in their numbers is 12.
• This translates into the equation: $a(a+4) - a^2 = 12$.
• Expanding and simplifying the left side, we have: $a^2 + 4a - a^2 = 12$.
• Simplify further: $4a = 12$.
• By dividing both sides by 4, we find: $a = 3$.

Using $a = 3$ to determine the number of students:

• Number of students who passed: $3(3 + 4) = 21$.
• Number of students who failed: $3^2 = 9$.
• Total number of students: $21 + 9 = 30$.

Therefore, the total number of students in the class is $\boxed{30}$.