Estimate the sum. Round each number to the nearest ten, then add.

To estimate the sum of \( 48 \frac{55}{82} + 54 \frac{41}{72} \), we first round each number to the nearest ten.

1. For \( 48 \frac{55}{82} \):
- The whole number part is \( 48 \), which rounds to \( 50 \).
- The fraction \( \frac{55}{82} \) is approximately \( 0.67 \) (since \( 55/82 \approx 0.671 \)). This can generally be considered as rounding to \( 0 \) since we're rounding to the nearest ten.
- So, \( 48 \frac{55}{82} \) rounds to about \( 50 \).

2. For \( 54 \frac{41}{72} \):
- The whole number part is \( 54 \), which rounds to \( 50 \).
- The fraction \( \frac{41}{72} \approx 0.57 \). This can also generally be considered as rounding to \( 0 \).
- So, \( 54 \frac{41}{72} \) rounds to about \( 50 \).

Now adding the rounded values:

\[
50 + 50 = 100
\]

Therefore, the estimate of the sum is \( \boxed{100} \).