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.

Answer 1

$$\begin{gathered} \begin{array}{l}\\ \text{Let the total number of students be}x.\end{array} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \frac{300}{x}-\frac{300}{x+10}=1 \\ \Rightarrow \frac{300(x+10)-300x}{x(x+10)}=1 \\ \Rightarrow \frac{300x+3000-300x}{x^2+10x}=1 \\ \Rightarrow 3000=x^2+10x \\ \Rightarrow x^2+10x-3000=0 \\ \Rightarrow x^2+(60-50)x-3000=0 \\ \Rightarrow x^2+60x-50x-3000=0 \\ \Rightarrow x(x+60)-50(x+60)=0 \\ \Rightarrow (x+60)(x-50)=0 \\ \Rightarrow x=50\text{or}x=-6\text{0} \\ x\text{cannot be negative; therefore, the total number of students is 50.} \end{gathered}$$