I set it up like this..

original cost per person is c = 420/n

new cost per person is c-3 = 420/(n+6)

I simplified the new cost equation to say (c-3)(n+6)=420

I then substituted "c" with 420/n like this

(420/n-3)(n+6)=420

I solved and got 26.13 students. How can 0.13 students go on the trip? I must have done something wrong.