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

A maths class takes an exam.

$a(a+4)$ of students passed, while $a^2$ failed the exam.

More students passed than failed and the difference between these numbers is 12.

How many students are in the class?

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 $\boxed{30}$.