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 student.
Solution:
Let the total number of students be $x$.
According to the question:
$\frac{300}{x}-\frac{300}{x+10}=1$
$\Rightarrow \frac{300(x+10)-300 x}{x(x+10)}=1$
$\Rightarrow \frac{300 x+3000-300 x}{x^{2}+10 x}=1$
$\Rightarrow 3000=x^{2}+10 x$
$\Rightarrow x^{2}+10 x-3000=0$
$\Rightarrow x^{2}+(60-50) x-3000=0$
$\Rightarrow x^{2}+60 x-50 x-3000=0$
$\Rightarrow x(x+60)-50(x+60)=0$
$\Rightarrow(x+60)(x-50)=0$
$\Rightarrow x=50$ or $x=-60$
$x$ cannot be negative; therefore, the total number of students is 50 .