Ascout troop planned to take a bus for an overnight trip to a campground in a nearby state. the bus will cost $360 to rent. the bus company told them that if they could get 3 more troop members to join in the trip each person could pay $6 less to go on the trip. if the troop was able to find the 3 additional people to join the trip, which answer is the most reasonable for the number of members that went on the trip?

Let x represent the number originally signed up.
.. 360/x -6 = 360/(x +3)
.. 360*(x +3) -6x(x +3) = 360x . . . . . multiply by the product of denominators
.. 360x +1080 -6x^2 -18x = 360x
.. x^2 +3x -180 = 0
.. (x +15)(x -12) = 0
Solutions are x = {-15, 12}

12 members went on the trip.

The problem wording does not make clear whether the original number (12) or the number suggested by the bus company (15) went on the trip. It would be most reasonable for 15 to go, if the troop had people who were willing.

Subtracting is the opposite of adding