Final answer:
The travel company will need 14 minibuses.
Step-by-step explanation:
To calculate the number of minbuses needed, we can divide the total number of passengers by the capacity of each minibus. Each minibus can carry 12 passengers.
Since the passengers can exactly fill 3 coaches and each coach can carry 53 passengers, the total number of passengers is 3 * 53 = 159.
Therefore, the number of minibuses needed is 159 / 12 = 13.25, which rounds up to 14 minibuses.
So, the travel company will need 14 minibuses.