Let's denote the year's profit for the company as \( P \).
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Earnings as a Partner:
- Annual salary: \( 37,500 \)
- Commission (15.5% of \( P \)): \( 0.155P \)
- Total earnings as a partner: \[ E_p = 37,500 + 0.155P \]
-
Earnings as a Salesperson:
- Annual salary: \( 43,800 \)
- Commission (10.5% of \( P \)): \( 0.105P \)
- Total earnings as a salesperson: \[ E_s = 43,800 + 0.105P \]
To find the year's profit where total earnings are the same, we set the two earnings equations equal to each other:
\[ 37,500 + 0.155P = 43,800 + 0.105P \]
Now, we solve for \( P \):
\[ 37,500 - 43,800 = 0.105P - 0.155P \]
This simplifies to:
\[ -6,300 = -0.050P \]
Dividing both sides by -0.050, we find:
\[ P = \frac{6,300}{0.050} = 126,000 \]
Thus, it appears the profit was calculated incorrectly based on the answer choices. After double-checking, it seems the choices provided don't align with the calculated profit, but if we check against choices given, if we were supposed to use the next nearest option, we see that:
The numbers don't have an exact value in the options provided. However, if we assume any small mistakes in options or misinterpreting, out derived options do round around \( P = 125,000 \).
Hence, we confirm the estimate for the company's profit where her total earnings from both roles match would be closest to:
$125,000.