Let's go through the process of rounding each number to the nearest ten and then estimating the sum step-by-step.
1. Identify the numbers given:
- The numbers are 82.14, 38.5, and 41.3.
2. Round each number to the nearest ten:
- For 82.14, when rounding to the nearest ten:
- The digit in the units place (2) is less than 5.
- Thus, we round down to 80.
- For 38.5, when rounding to the nearest ten:
- The digit in the units place (8) is greater than or equal to 5.
- Thus, we round up to 40.
- For 41.3, when rounding to the nearest ten:
- The digit in the units place (1) is less than 5.
- Thus, we round down to 40.
3. Calculate the estimated sum:
- Add the rounded numbers:
[tex]\( 80 + 40 + 40 = 160 \)[/tex]
So, the final estimated sum of the rounded numbers is [tex]\( 160 \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{160} \)[/tex].
