Amy has a choice of two different positions at a new company. As a partner, she can receive

Question

an annual salary of $37,500 plus 15.5% of the year’s profit for the company. As a salesperson,
she can receive an annual salary of $43,8000 plus 10.5% of the year’s profit for the company.
Estimate the year’s profit for the company for which her total earnings for the year are the
same in either position.
(1 point)
$60,000
$125,000
$175,000
$57,000

Answer 1

Let's denote the year's profit for the company as \( P \).

1. Earnings as a Partner:

   • Annual salary: \( 37,500 \)
   • Commission (15.5% of \( P \)): \( 0.155P \)
   • Total earnings as a partner: \[ E_p = 37,500 + 0.155P \]

2. 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.