Final answer:
To determine the total number of rooms needed, add the initial number of rooms reserved to the additional rooms required.
Step-by-step explanation:
To determine the total number of rooms needed, we need to find the sum of the initial number of rooms reserved and the additional rooms required.
Let's assume the initial number of rooms reserved was 50. If the company increases the number of people going on the trip, we can represent this as an equation: 50 + x, where x represents the additional number of rooms required.
If the company needs at least 56 rooms in total, the equation would be: 50 + x = 56. By subtracting 50 from both sides, we find that x = 6. Therefore, Joe needs to reserve at least 6 additional rooms for a total of 56 rooms.