Question 998781
So , hiring the transportation for the {{{n}} students who planned to make the trip costs {{{225000}}} ,
and the cost per student is {{{225000/n}}} .
However, since they have some free seats on the hired transportation,
they could transport {{{5}}} more students for the same total cost.
Then, the cost per student would be {{{225000/(n+5)}}} .
If that is {{{500}}} less, that means that
{{{225000/n-225000/(n+5)=500}}}
Multiplying both sides of the equal sign times {{{n*(n+5)}}} (which is not zero),
we get the equivalent equation
{{{225000(n+5)-225000n=500*n*(n+5)}}}
{{{225000n+225000*5-225000n=500*n*(n+5)}}}
{{{225000*5=500*n*(n+5)}}}
{{{225000*5/500=n*(n+5)}}}
{{{2250=n*(n+5)}}}
Now, you have to solve that equation.
You could see that it is a quadratic equation,
you could re-write it in a more traditional form,
as {{{n^2+5n-2250=0}}} ,
and solve it whichever way will make your teacher satisfied
(factoring, completing the square, or using the quadratic formula).
Alternatively, from {{{2250=n*(n+5)}}} ,
you could look for factors {{{n}}} and {{{(n+5)}}} whose product is {{{2250}}} ,
and finding that {{{45*50=2250}}} ,
you would conclude that {{{system(n=highlight(45),n+5=50)}}} .
So {{{highlight(45)}}} students planned to make the trip.