Use the image to answer the question.

Question

Two lines are graphed on the coordinate plane.

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

$175,000
$175,000

$60,000
$60,000

$57,000
$57,000

$125,000

Answer 1

To find the year's profit for the company where Amy's total earnings are the same in both positions, we can set up the equations for her earnings in each position and solve for the profit.

Let \( P \) represent the profit for the company.

1. Earnings as a Partner: \[ E_P = 37500 + 0.155P \]

2. Earnings as a Salesperson: \[ E_S = 43800 + 0.105P \]

Set these two equations equal to each other to find the profit \( P \): \[ 37500 + 0.155P = 43800 + 0.105P \]

Subtract \( 0.105P \) from both sides: \[ 37500 + 0.050P = 43800 \]

Now, subtract 37500 from both sides: \[ 0.050P = 6300 \]

Now, divide both sides by 0.050: \[ P = \frac{6300}{0.050} = 126000 \]

It seems that the options listed do not directly match our calculated value of \( 126,000 \). The closest possible answer based on options given appears to be missing, but if we double-check only the typical response options provided:

1. $175,000
2. $60,000
3. $57,000
4. $125,000

Correct Response: $125,000 (since it is the closest reasonable option available, based on the calculation and typical salary scenarios.)