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. Determine the number of students.

Answer 1

Let the number of students be $x$. Then,

Share of each student = $\frac{300}{x}$

If there were $x+10$ students, then,

Share of each students = $\frac{300}{10+x}$

According to question,

$\frac{300}{x}-\frac{300}{x+10}=1$

$x^2+10x=3000$

$x^2+10x-3000=0$

$(x+60)(x-50)=0$

$x=50$

Therefore, the number of students is $50$.