Question

Ernie earned $121.50 more than Kaylin. Tria earned $35 less than 3 times the amount Kaylin earned. Ernie, Tria, and Kaylin earned $579 in all. How much did Tria earn?

Answer 1

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 \(\boxed{260.50}\).