Question

Ranjana wants to distribute $540$ oranges among some students. If $30$ more students are added each would get $3$ oranges less. Find the number of students

Answer 1

Total oranges$=540$

Let the total number of students be $x$Orange each studnt gets$=\frac{540}{x}$

If $30$ more students are there so, the total number of students will be $x+30$

Number of oranges per person will be $\frac{540}{x+30}$

if $30$ students were more each would get $3$ oranges less$=\frac{540}{x}-3$

$\Rightarrow \frac{540}{x+30}=\frac{540}{x}-3$

$\Rightarrow 540x=(540-3x)(x+30)$

$\Rightarrow 3x^2+90x-16200=0$

$\Rightarrow x^2+30x-5400=0$

$\Rightarrow x^2+90x-60-5400=0$

$\Rightarrow (x+90)(x-60)=0$

$\therefore x=-90,60$

But number of students cannot be negative,so the number of students is $60$