Question 119284
Let N be the number of students originally going. 
Let P be the per-person cost of the trip. 
{{{2250/N=P}}}
{{{2250/(N+5)=P-5}}}
{{{2250/(N+5)=2250/N-5}}}
{{{2250N=2250(N+5)-5N(N+5)}}}
{{{2250N=2250N+11250-5N^2-25N}}}
{{{0=-5N^2-25N+11250}}}
{{{N^2+5N-2250=0}}}
{{{(N+50)(N-45)=0}}}
N must be positive
{{{N=45}}}
Originally 45 students planned to take the trip, costing $50 each.
Now 50 students are taking the trip, costing $45 each or $5 less.