Let \( K \) represent the amount Kaylin earned.
According to the problem:
- Ernie earned \( K + 121.50 \)
- Tria earned \( 3K - 35 \)
The total earnings of Ernie, Tria, and Kaylin is given by:
\[ (K + 121.50) + (3K - 35) + K = 579 \]
Let's simplify the left side:
\[ K + 121.50 + 3K - 35 + K = 579 \] \[ 5K + 86.50 = 579 \]
Now, subtract 86.50 from both sides:
\[ 5K = 579 - 86.50 \] \[ 5K = 492.50 \]
Next, divide both sides by 5 to solve for \( K \):
\[ K = \frac{492.50}{5} \] \[ K = 98.50 \]
Now that we have the value for Kaylin's earnings, we can calculate Tria's earnings:
\[ \text{Tria's earnings} = 3K - 35 = 3(98.50) - 35 \] \[ = 295.50 - 35 \] \[ = 260.50 \]
Thus, Tria earned \(\boxed{260.50}\).
To verify, we can calculate Ernie's earnings as well:
\[ \text{Ernie's earnings} = K + 121.50 = 98.50 + 121.50 = 220 \]
Now, we can check the total earnings:
\[ \text{Total} = K + \text{Ernie's earnings} + \text{Tria's earnings} = 98.50 + 220 + 260.50 = 579 \]
Since this total matches the given condition, our calculations confirm that Tria earned \(\boxed{260.50}\).