a wagon train had ninety-six wagons each carrying the same number of people.
when twelve broke down, each of the other wagons had to carry one more person.
How many people were in each wagon originally.
This problem can be solved using arithmetic or algebra.
Arithmetic:
96 wagons, of which 12 broke down.
So there are 84 left, each taking in one more passenger.
So the 12 non-functioning wagons carried 84 passengers, therefore 7 in each wagon.
Algebra:
Let x be the number of passengers on each wagon originally.
So
96x=84(x+1)
Solve for x:
96x=84x+84
(96-84)x=84
x=84/12=7 passengers.