Understanding the problem:
We are given that a 3-digit number was rounded off to the nearest ten and the rounded number is 320. We need to determine the interval of the original number.

Key Points:
- To round off a number to the nearest ten, we look at the digit in the ones place.
- If the ones digit is 0, 1, 2, 3, or 4, we round down to the previous ten.
- If the ones digit is 5, 6, 7, 8, or 9, we round up to the next ten.

Solution:
To find the interval of the original number, we need to consider the possible values that could have been rounded to 320.

Step 1: Understand the Rounding Process
- When a number is rounded to the nearest ten, we look at the digit in the ones place.
- If the ones digit is 0, 1, 2, 3, or 4, we round down to the previous ten.
- If the ones digit is 5, 6, 7, 8, or 9, we round up to the next ten.

Step 2: Find the Lower Limit
- Since the rounded number is 320, we know that the original number could have been rounded down from a number between 315 and 324.
- The original number could have been any number between 315 and 324, as long as the ones digit is between 0 and 4.

Step 3: Find the Upper Limit
- To find the upper limit, we consider the possible values that could have been rounded up to 320.
- The ones digit of the original number must be between 5 and 9 to round up to 320.
- Therefore, the original number could have been any number between 325 and 329, as long as the ones digit is between 5 and 9.

Step 4: Determine the Interval
- The interval of the original number is the range between the lower limit and the upper limit.
- In this case, the lower limit is 315 and the upper limit is 329.
- Therefore, the interval of the original number is 315 to 329.

Answer:
The interval of the original number is 315 to 329.