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=x^2+10x` 

⇒`x^2+10x-3000=0` 

⇒`x^2+(60-50)x=3000=0` 

⇒`x^2+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.