Question

300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Answer 1

Let the total number of students be x. 

According to the question:  

`300/x - 300/(x + 10) = 1` 

⇒ `(300(x + 10) - 300x)/(x(x + 10)) = 1` 

⇒ `(300x + 3000 - 300x)/(x^2 + 10x) = 1` 

⇒ 3000 = x² + 10x 

⇒ x² + 10x – 3000 = 0 

⇒ x² + (60 – 50)x = 3000 = 0 

⇒ x² + 60x – 50x – 3000 = 0 

⇒ x(x + 60) – 50(x + 60) = 0 

⇒ (x + 60)(x – 50) = 0 

⇒ x = 50 or x = –60 

x cannot be negative; therefore, the total number of students is 50.