In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.

Let the number of rows be x

So, the number of students in each row = x + 4

Given, total students = 480

$\Rightarrow x(x + 4) = 480 \\[1em] \Rightarrow x^2 + 4x = 480 \\[1em] \Rightarrow x^2 + 4x - 480 = 0 \\[1em] \Rightarrow x^2 + 24x - 20x - 480 = 0 \\[1em] \Rightarrow x(x + 24) - 20(x + 24) = 0 \\[1em] \Rightarrow (x - 20)(x + 24) = 0 \\[1em] \Rightarrow x - 20 = 0 \text{ or } x + 24 = 0 \\[1em] x = 20 \text{ or } x = -24.$

Since number of rows cannot be negative hence, x ≠ -24.

If x = 20 , x + 4 = 24.

Hence the number of students in each row are 24.